Focus: Electron Spin Influences Nanotube Motion
The spin of an electron often occupies a reality all its own, with little bearing on the electron’s overall motion or the motion of nearby atoms. But theoretical work reported in Physical Review Letters demonstrates that the spin of a single electron trapped on a carbon nanotube may influence—and be influenced by—the vibrations of the nanotube. The researchers behind the work foresee this spin-mechanical combination having a role in nanoscale mass sensors or in information processing elements of a quantum computer.
Electron spin sometimes makes its presence known in subtle ways. A single energy level in an atom can become two closely spaced levels because of so-called spin-orbit coupling. In this effect, the motion of the electron around the nucleus creates an effective magnetic field that causes spin-up electrons to have a slightly different energy from spin-down electrons. A similar sort of spin-orbit coupling was recently discovered in carbon nanotubes . The delocalized electrons, those not associated with specific atoms, follow circular orbits around the tube circumference. As in an atom, this motion causes one orientation of the electron spin to have lower energy than the opposite orientation.
This relationship between the electron spin and the cylindrical geometry of a nanotube means that motion of the tube could alter the spin, and vice versa. András Pályi of Eötvös University in Budapest and his colleagues have now proposed an experiment to demonstrate this connection. The proposal is based on recent work examining the relationship between nanotube motion and electric current .
In their model, the team imagines a carbon nanotube suspended between two leads about a half micron apart, with a single electron trapped on this “tightrope.” An externally applied magnetic field pointing along the nanotube axis splits the ground state of the electron into two energy levels, corresponding to the electron spin being parallel and antiparallel to the magnetic field.
As in earlier work, vibrations in the nanotube can be excited by radio waves tuned to one of the resonant frequencies. The changes in the shape of the nanotube alter the orbital path of the trapped electron, and because of the strong spin-orbit coupling, the electron’s spin can switch direction . In order to maximize the effect on the spin, the theorists found that the magnetic field strength must be set so that the energy difference between the two spin states matches the energy of the nanotube vibration.
Pályi and his colleagues found that the system mimics the well-studied case of an atom in an optical cavity, where the atom can only emit or absorb light for which an integer number of half-wavelengths matches the cavity’s length. Similarly, in the sound wave (or phonon) cavity of the stretched nanotube, transitions between the two spin states are driven by nanotube vibrations. And the influence goes both ways, as numerical calculations showed that the coupling to a single electron spin shifts the frequency at which the nanotube vibrates.
The team says that adding such a spin-dependence could improve the sensitivity of nanotube-based sensors that can already measure the mass of a handful of atoms. In quantum computing, the oscillations of the nanotube could be used to flip the value of a spin qubit or process it in some way. Since the nanotube motion can be driven by simple radio waves from a small antenna, this qubit control might be less challenging than other techniques that rely on rapidly varying magnetic fields, Pályi says.
“This is a promising hybrid system, and experiments are making rapid progress, placing novel proposals like this in high demand,” says Steven Bennett from Harvard University. One challenge is measuring the vibrations in the nanotube, says Gary Steele from the Technical University of Delft in the Netherlands. Typically this tiny motion has been observed using currents through the nanotube, but the goal here is to keep electrons in place on the nanotube. Developing external detectors of nanotube motion is “a very challenging task,” Steele says, but one that he and others are working on right now.
Michael Schirber is a freelance science writer in Lyon, France.
- F. Kuemmeth, S. Ilani, D. C. Ralph, and P. L. McEuen, “Coupling of Spin and Orbital Motion of Electrons in Carbon Nanotubes,” Nature 452, 448 (2008)
- G. A. Steele, A. K. Huttel, B. Witkamp, M. Poot, H. B. Meerwaldt, L. P. Kouwenhoven, and H. S. J. van der Zant, “Strong Coupling Between Single-Electron Tunneling and Nanomechanical Motion,” Science 325, 1103 (2009)
- D. V. Bulaev, B. Trauzettel, and D. Loss, “Spin-Orbit Interaction and Anomalous Spin Relaxation in Carbon Nanotube Quantum Dots,” Phys. Rev. B 77, 235301 (2008)


Jonathan Santiago, of MIT, describes his experience working with GreenFab and teaching advanced technical concepts to students in the Bronx. Here, A student experiments with using an Arduino microcontroller to power LEDs.
Credit: Jonathan Santiago, STEM2GETHER
This Behind the Scenes article was provided to LiveScience in partnership with the National Science Foundation.
Growing up I was always very good at using computers, but I never really understood how they worked. Until I began my undergraduate studies at MIT, I never made the connection between what happens inside a desktop computer and what happens inside other everyday electronic devices. I didn't know what micro-controllers were, or how they've been used in TV remotes, MP3 players, cell phones, space shuttles, medical devices, and of course, personal computers.
Now I help teach embedded electronics, also known as physical computing, and digital fabrication to high school students in the South Bronx section of New York City. Going to school in the country's poorest congressional district, the students who participate in the NSF funded GreenFab program have had no shortage of obstacles to their academic success. Despite these challenges, we don't doubt for a moment that we can teach our students advanced technical concepts, and inspire many of them to pursue careers in green technology and engineering.
Although I now have a better understanding of embedded processing and enjoy teaching physical computing and digital fabrication to our students, I still have vivid memories of what it felt like to be completely in the dark. The late science fiction author Arthur C. Clarke once said that, "Any sufficiently advanced technology is indistinguishable from magic." If that's the case, then I felt during my first year at MIT that the engineers and scientists I met were indistinguishable from sorcerers. Some of the projects that were underway in Neil Gershenfeld's Center for Bits and Atoms research group (also NSF funded) included NMR quantum computing, inertial measurement devices, liquid computers, new internet protocols for household objects, and the creation of low-cost digital fabrication laboratories around the world.
Involvement with the latter project, called FabLabs, is what led me to work for Sustainable South Bronx and Vision Education & Media to teach kids. FabLabs began as an outreach project from the Center for Bits and Atoms (CBA) group. They have a mission to provide widespread access to Computer Numerically Controlled (CNC) fabrication equipment and other modern tools for invention.
An international network of FabLabs is currently evolving, with activities ranging from youth technology enrichmenment programs to the incubation of small-scale high-tech businesses.
Working with FabLab tools during my undergraduate research at MIT was actually more helpful in demystifying how things are made and how things work than the introductory electrical engineering and computer science classes I took before I switched my major to mathematics. Those introductory classes focused heavily on first principles and abstract concepts, postponing hands on work until a theoretical framework was learned. FabLabs take the opposite approach. You learn concepts as they become necessary. FabLabs provide a great opportunity to make engineering and science hands-on for kids, rather than remote and abstract.
Since the program began this past February, there is one student who stands out as an example.
At first, Jose was somewhat of a challenging student to work with. Obviously a bright kid without a lot of energy, he wasn't always able to maintain focus and attention on any particular task. He saw everything as complicated and difficult, often giving up very early. Jose made a noticeable transformation during this past summer session, after building a DIY (do-it-yourself) robot project from scratch. I told Jose and a few other students to look up the Arduino SERB robot, which could be made from sratch using equipment and parts that we either had in the lab or could be easily obtained.
Jose found a great tutorial on Instructables.com on how to put the robot together. With a minimal amount of supervision, Jose was able to finish the project and even add his own variation. He wanted the robot to be controlled by a Nintendo Wii 'Nunchuck' controller, which uses an accelerometer to control a gaming interface. Taking his own initiative, he researched how to 'hack' the Wii controller to have it interface with the SERB robot.
Jose is currently a senior in high school and has expressed a strong desire to pursue an engineering degree at the New York State University at Buffalo, citing GreenFab as a motivating factor in his career ambitions.
At the very least, we hope that when the students complete our program they will have acquired independent learning skills and a penchant for questioning how things work. This might lead to questioning how other complicated systems work, such as urban politics, development, and infrastructure. GreenFab could lead them to ask questions like, "Why are there less Green Spaces in the South Bronx than the West Village?," "Why does the city want to build more prisons and waste handling facilities in my neighborhood?," or "Saving polar bears is cool and everything, but can the 'green' movement actually help me earn a decent living?"
The GreenFabWinter Project Exhibition will be December, 21 4:00 – 6:00 p.m. at 841 Barretto Street in the Bronx.
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Editor's Note: This research was supported by the National Science Foundation (NSF), the federal agency charged with funding basic research and education across all fields of science and engineering. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. See the Behind the Scenes Archive.


How do you predict how a given quantum state (which always corresponds to a single point anywhere on or in the sphere) will react if subjected to a given quantum measurement (which always corresponds to a single axis)? To see how, draw a new line perpendicular to the measurement axis and passing through the point corresponding to the quantum state. The new line will divide the measurement axis into two segments whose lengths correspond to the probabilities of the two possible measurement results. An example:
This figure shows a measurement that corresponds to tilting your polarizer (for example, sunglasses) by 55 degrees, and gives a 20% chance of measuring state (2) and an 80% chance of measuring state (1).
This is now the third or fourth time we've encountered some type of measurement which gives random results. This is the first classical assumption that we have to let go:
Classical Theory: God does not play dice with the universe.
Quantum Theory: Quantum measurement can give random results.
Are these results truly random, or did we just not know the answer before performing the measurement? This is very similar to asking the question, "If you measure the same qubit many times, do you get the same answer?" Answer: If you perform the same measurement, you always get the same result. Only the first measurement result is (potentially) random.
Wait a minute. That doesn't seem right.
Let's say I measure a photon several times in a row using the red, green, and blue axes (horizontal, diagonal, and right-circular polarizers) and every time the photon is transmitted. 100 percent horizontal, 100 percent diagonal, 100 percent right-circular? Remember that we are plotting each point using the answers to those three questions. Plotting 100 percent/100 percent/100 percent will give a point far outside the sphere, a state forbidden by quantum mechanics. Can we really never obtain these results, or is quantum mechanics wrong about the sphere? Neither. This is a false choice, because it's based on our second false assumption about classical information—an assumption that doesn't apply to qubits:
Classical Theory: Reading the value of a bit doesn't change the bit's value.
Quantum Theory: Measuring a qubit changes its value to match the result of the measurement.
Using this newfound principle of quantum information, let's walk through an example. Let's start with a horizontally polarized photon, H. If we measure this photon using the H/V axis, it will stay horizontally polarized. If we then perform a measurement on the green axis, it is randomly transformed into either D or A (we'll choose D for this example). Finally, we repeat our first measurement using the red axis. Instead of giving the same result as our first measurement, however, there's now a 50 percent chance that our horizontal photon will be measured as vertical! The intervening measurement has changed the state of the qubit. (It's worth noting here that measurement is a real process, the same process that polarizing sunglasses and 3D lenses perform. You can test all of these examples with just a few pairs of eyewear.)
Measurement appears, strangely, to be one way we can change the state of a qubit. For a quantum programmer wanting to adjust the qubits in a quantum computer, however, this may not be a good choice. After all, the results are random! Although some exotic quantum algorithms use measurement in the middle of a computation, most of the time measurement is reserved for the end, when the programmer learns the result of the computation.
How then, do we change qubits without introducing randomness? Physically, every species of qubit (photon, electron, ion, etc.) is changed differently. Photon polarization can be changed by directing a photon through quartz crystals or Scotch tape. All of these processes, regardless of the species of qubit or the type of change, have a simple interpretation on the single-qubit sphere: they act as rotations.
These rotations are defined by a single axis, just like measurements. But, instead of projecting all possible states into two possible outcomes, they rotate all states on an axis. Only the points on the axis of rotation will be unaffected. As an example, think of rotating the sphere by 90 degrees about the red axis. This kind of quantum operation leaves H and V unchanged, but transforms R > D, D > L, L > A, and A > R.
We can now summarize the important characteristics of single qubits:
- All single-qubit states correspond to a point on or inside a sphere.
- Every axis corresponds to a single quantum measurement, and
every measurement changes the state of the qubit to match the
result of the measurement.
- Qubits can be changed by rotating them around an axis.
Although this succinctly describes the way in which a one-qubit quantum computer is supposed to work, what happens when things go wrong? For a classical bit, the only thing that can go wrong is for a bit to unexpectedly flip from zero to one or one to zero. The same type of thing could happen to qubits, in the form of unexpected or unwanted rotations. But there's another type of process, one that researchers in quantum computing are constantly fighting to eliminate: decoherence.
Decoherence happens when something outside of the quantum computer performs a measurement on a qubit, the result of which we never learn. Let's say we measure the state H in the D/A axis (the green) axis. There's a 50% chance of measuring H in the state D and a 50% chance of measuring it in the state A. If we never learn which state the measurement resulted in, we'll have no idea how to predict the result of another measurement.
This process is called decoherence, and, in fact, it's how states inside the sphere are created. By measuring along an axis but never learning the result, all points on the sphere collapse to the measurement axis. By partially measuring something (with say, really thin polarized sunglasses), we can collapse only part of the way:
This sort of unwanted intrusion introduces randomness into a quantum computer. Because quantum bits can be single electrons, single ions, or single photons, all of which can be accidentally measured using a single stray atom, it can be exquisitely difficult to avoid decoherence. That's the primary reason that a 100-qubit quantum computer has not yet been built.


Speed of light
The speed of light in vacuum is held to be constant at 299,792,458 m/s (186,282.397 miles per second). Designated by the symbol "c" (for "constant"), it is a fundamental quantity of the universe. According to special relativity it is the universe's speed limit and it is part of the relation between mass and energy:
Some have proposed that the speed of light has decayed since the Creation. While this theory opened the door to scientific solutions to the distant starlight problem, it is not generally accepted by creation scientists.
One-Way Speed of Light
Sagnac proved that light travels at different speeds depending on its direction and its proximity to the center of Earth's gravity, lending weight to the Anisotropic convention.
The one-way speed of light has never been measured. Every known measurement of the speed of light includes reflecting it from another surface. This necessarily changes the nature of light, as it can only be the average of the outbound and inbound leg. Additionally, all electronic means to measure the speed of light cannot themselves operate at the speed of light. This introduces error and constraint into the measurement. If we attempt to embed a signal into a light beam to synchronize two clocks at a distance, the time it takes to both create and to interpret the signal introduce another constraint. In fact, any introduction of a measurement mechanism necessarily constrains the measurement because no measurement mechanism can operate at the speed of light.
Einstein understood the primary paradox of the speed of light, as evidenced by the theory of black holes. A black hole's gravity is so strong that light cannot reach escape velocity. However, gravity can only act in this manner between bodies with mass, which necessarily means that photons have mass. Physicists generally do not accept the notion that photons have mass. If they do not, they would be able to escape a black hole, and it would not be black after all. However, if the photon has mass, then it is a particle with mass traveling at the speed of light. For such particles, time stands still. There is no duration between their departure (from an emitting source) and their destination. Essentially departure and arrival are instantaneous. If this is the case with a photon, then there is no such thing as a light-year in space, and the age of the Cosmos cannot be determined using light as a basis. Moreover, the speed of light is a function of distance and duration: speed = distance/time. However, Einstein asserted that time is relative. If this is true then the speed of light is also relative and cannot be constant.
To resolve this paradox, Einstein side-stepped it by stipulating that the speed of light is constant without ever proving it.
That light requires the same time to traverse the path A > M as for the path B > M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity" (Einstein 1961, p. 23) [emphasis is in the original].
Whenever scientists encounter particle behaviors that defy the speed of light, such as the propensity of particles to instantly share behaviors even across vast distances (e.g. Quantum Entanglement) they still hold to the notion that the speed of light is constant, eliciting the strangest explanations, including the idea that all particles in the universe are connected to all other particles through wormholes. Such oddball theories are the simplest evidence that the "constant" speed of light has been accepted as a reality rather than a stipulation for mathematical purposes.
Albert A. Michelson is credited with developing the method for the definitive measurement of the speed of light. In 1902 he published his classic paper on the speed of light, and in 1907 was awarded the Nobel Prize in Physics for this work. Michelson also proposed the standardization of the international unit of length, the meter, using specified wavelengths of light rather than an artifact. For decades the scientific community used Michelson's standardization method, but finally decided to define the SI unit of length according to the speed of light. Today one meter is defined as exactly 1/299,792,458 of the distance that a beam of light travels in one second.
Many scientists in the past have speculated about possible changes in the values of one or more physical constants and its implications. These speculations were not always greeted with enthusiasm from the scientific community because the implications of any variation in any constant are enormous: it would introduce changes at astronomical levels in the very fiber of the Universe. Yet the idea never totally died out and was never totally suppressed.
Glenn Morton was one of the first persons to put forth a concrete and testable model. He started not from changing fundamental constants, but from another angle. Soon Barry Setterfield came forward with his proposal of variation in the velocity of light. His initial proposal went through several revisions and modifications and creationist publications quoted him widely. Some secular publications also used the information, but the general response was to resist his proposals.
Johnson C. Philip from India put forth the same idea in a broader way in 1982 and did some work with the Physics department of Jiwaji University in India. However, he had to abandon the work in 1984 due to the resistance of some non creationist professors.
The proposal remains promising, and much work can be done. The resistance remains, especially from non creationists. However, the topic might find a revival, now that the secular community has started to consider the idea of changing fundamental constants.
The speed of light has been used to calculate the distance of supernova 1987A from earth with great accuracy, based on observing the time taken for its light to illuminate the Large Magellanic Cloud. It is the standard method for calculating the distance to nearby galaxies.
The part of the SN1987A ring perpendicular to the explosion center (as seen from us) was observed to light up about 8 months after the explosion. The light that took a detour via the ring to us was always a ring radius behind the direct light regardless of the speed of light that prevailed during the trip. The ring radius could be calculated to these 8 months times the speed of light as applied to the year 1987, when the measurement was made. Thus it is not of this observation to deduce if the light has had any different speed before 1987.
The notion of c-decay is currently out of favor even among creationists. Two models for the creation of the universe, i.e. white hole cosmology and cosmological relativity, both assume a constant value of c.
The Anisotropic Synchrony Convention holds for a variable value for c, and likewise provides for c to be relative to the speed of the emitting object. Anisotropism is the actual de-facto convention for Scripture, as God describes things from a human's-eye point-of-view. Even Christ said he would use earthly things to describe heavenly things. The human point-of-view is integrated to the Anisotropic convention, providing for the instantaneous arrival of distant starlight as well as explain local measurement in terms of time dilation.
- Biography of Albert A. Michelson from the Nobel Committee
- An Alternate View of SN1987A by Selva Harris.
- Speed of light may have changed recently by Eugenie Samuel Reich, NewScientist.com


First Electronic Quantum Processor Created
A team led by Yale University researchers has created the first rudimentary solid-state quantum processor, taking another step toward the ultimate dream of building a quantum computer.
The two-qubit processor is the first solid-state quantum processor that resembles a conventional computer chip and is able to run simple algorithms. (Credit: Blake Johnson/Yale University)
They also used the two-qubit superconducting chip to successfully run elementary algorithms, such as a simple search, demonstrating quantum information processing with a solid-state device for the first time. Their findings appeared in Nature's advanced online publication June 28.
"Our processor can perform only a few very simple quantum tasks, which have been demonstrated before with single nuclei, atoms and photons," said Robert Schoelkopf, the William A. Norton Professor of Applied Physics & Physics at Yale. "But this is the first time they've been possible in an all-electronic device that looks and feels much more like a regular microprocessor."
Working with a group of theoretical physicists led by Steven Girvin, the Eugene Higgins Professor of Physics & Applied Physics, the team manufactured two artificial atoms, or qubits ("quantum bits"). While each qubit is actually made up of a billion aluminum atoms, it acts like a single atom that can occupy two different energy states. These states are akin to the "1" and "0" or "on" and "off" states of regular bits employed by conventional computers. Because of the counterintuitive laws of quantum mechanics, however, scientists can effectively place qubits in a "superposition" of multiple states at the same time, allowing for greater information storage and processing power.
For example, imagine having four phone numbers, including one for a friend, but not knowing which number belonged to that friend. You would typically have to try two to three numbers before you dialed the right one. A quantum processor, on the other hand, can find the right number in only one try.
"Instead of having to place a phone call to one number, then another number, you use quantum mechanics to speed up the process," Schoelkopf said. "It's like being able to place one phone call that simultaneously tests all four numbers, but only goes through to the right one."
These sorts of computations, though simple, have not been possible using solid-state qubits until now in part because scientists could not get the qubits to last long enough. While the first qubits of a decade ago were able to maintain specific quantum states for about a nanosecond, Schoelkopf and his team are now able to maintain theirs for a microsecond—a thousand times longer, which is enough to run the simple algorithms.
To perform their operations, the qubits communicate with one another using a "quantum bus"—photons that transmit information through wires connecting the qubits—previously developed by the Yale group.
The key that made the two-qubit processor possible was getting the qubits to switch "on" and "off" abruptly, so that they exchanged information quickly and only when the researchers wanted them to, said Leonardo DiCarlo, a postdoctoral associate in applied physics at Yale's School of Engineering & Applied Science and lead author of the paper.
Next, the team will work to increase the amount of time the qubits maintain their quantum states so they can run more complex algorithms. They will also work to connect more qubits to the quantum bus. The processing power increases exponentially with each qubit added, Schoelkopf said, so the potential for more advanced quantum computing is enormous. But he cautions it will still be some time before quantum computers are being used to solve complex problems.
"We're still far away from building a practical quantum computer, but this is a major step forward."
Authors of the paper include Leonardo DiCarlo, Jerry M. Chow, Lev S. Bishop, Blake Johnson, David Schuster, Luigi Frunzio, Steven Girvin and Robert Schoelkopf (all of Yale University), Jay M. Gambetta (University of Waterloo), Johannes Majer (Atominstitut der Österreichischen Universitäten) and Alexandre Blais (Université de Sherbrooke).
Article source: ScienceDaily.com
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We have been delving into the dirty secret behind our food, which is that it comes from bacteria, primarily, with considerable assistance from a social network of fungi, nematodes, micro-arthropods and soil-dwelling microbes of various descriptions, many of which make the Star Wars café scene characters seem tame. Most people, asked what plants eat, answer something like, “sunlight, water and dirt.” Water and sunlight play an important role, for sure. Using the energy of photons from the sun, sugars and carbohydrates are constructed from carbon dioxide and water, discarding oxygen. But the real denizens of the deep are bacteria.
Thanks to O2-generating bacteria at work for a billion years, Earth is now habitable for oxygen-loving creatures such as ourselves.
In general terms, the strategy for solar energy utilization in all organisms that contain chlorophyll or bacteriochlorophyll is the same. Here is how some of our ancestors, the purple bacteria, do it:
- Light energy is captured by pigment molecules in the light harvesting or "antenna" region of the photosystem, and is stored temporarily as an excited electronic state of the pigment.
- Excited state energy is channeled to the reaction center region of the photosystem, a pigment-protein complex embedded in a charge-impermeable lipid bilayer membrane.
- Arrival of the excited state energy at a particular bacteriochorophyll (BChl), or pair of BChls in the reaction center triggers a photochemical reaction that separates a positive and negative charge across the width of the membrane.
- Charge separation initiates a series of electron transfer reactions that are coupled to the translocation of protons across the membrane, generating an electrochemical proton gradient [protonmotive force (pmf)] that can be used to power reactions such as the synthesis of ATP.
If your eyes glazed over at that explanation, don’t worry. Much of photosynthesis still remains a mystery. Over the past several decades scientists examining oxygenic bacteria known as prochlorophytes (or oxychlorobacteria) have discovered a light harvesting protein complex. The intriguing thought arises, given how much of the bodies of plants are actually made up of bacteria (as also are our own), of whether photosynthesis is actually dependent on bacteria at one or more of the steps in the process.
Recently Drs. Jianshu Cao, Robert Sibley and three MIT graduate students studied purple bacteria, one of the planet’s oldest species, and discovered a special symmetry. Ring-shaped molecules are arranged in a peculiarly faceted pattern on the spherical photosynthetic membrane of the bacterium. Dr. Cao says, “We believe that nature found the most robust structures in terms of energy transfer." Only a lattice made up of nine-fold symmetric complexes can tolerate an error in either direction.
Spinning Photon Nets
Another discovery (by Sabbert et al. in 1996) is that in order to optimize sunlight, the nine-fold symmetric lattice has to spin. Moreover, it has to spin quite fast — nearly 100 rpm. We know of some bacterial flagella that spin at high rpm. Might spinning flagella propel the photon-capturing process? Too soon to say, but its an intriguing idea, and yet more evidence for quantum entanglement of all life, big and small.
The Encyclopedia of Applied Physics (1995) says:
The amount of CO2 removed from the atmosphere each year by oxygenic photosynthetic organisms is massive. It is estimated that photosynthetic organisms remove 100 x 1015 grams of carbon (C)/year. This is equivalent to 4 x 1018 kJ of free energy stored in reduced carbon, which is roughly 0.1% of the incident visible radiant energy incident on the earth/year. Each year the photosynthetically reduced carbon is oxidized, either by living organisms for their survival, or by combustion. The result is that more CO2 is released into the atmosphere from the biota than is taken up by photosynthesis. The amount of carbon released by the biota is estimated to be 1-2 x 1015 grams of carbon/year. Added to this is carbon released by the burning of fossil fuels, which amounts to 5 x 1015 grams of carbon/year. The oceans mitigate this increase by acting as a sink for atmospheric CO2. It is estimated that the oceans remove about 2 x 1015 grams of carbon/year from the atmosphere. This carbon is eventually stored on the ocean floor. Although these estimates of sources and sinks are uncertain, the net global CO2 concentration is increasing. Direct measurements show that each year the atmospheric carbon content is currently increasing by about 3 x 1015 grams. … Based on predicted fossil fuel use and land management, it is estimated that the amount of CO2 in the atmosphere will reach 700 ppm within [this] century. (references omitted)What needs to happen, quickly, to reverse our rush to a climate from which there can be no near-term recovery, and to avoid Earth becoming as uninhabitable as Venus, is to accelerate photosynthesis while decelerating carbon emissions. Our allies in this are bacteria and fungi, as they were billions of years ago. They will do the heavy lifting if we just give them a little support. They need good growth conditions (like heat and moisture, which we should have in increasing abundance this century), nutrients, and space to breathe. Lose the antibacterial soaps and sprays, please.
Planting gardens and tree crops is a start. Ecological restoration, where damage can be slowly unwound by greenery, is another step. Living roofs, tree-lined hardscapes, earth-sheltered homes: all of these are both adaptive and mitigating strategies for a recovering climate stasis. But there is something even more powerful.
Tea from a Firehose
This week we asked Joey “Mr Tea” Thomas to come dose the Ecovillage Training Center with his eclectic brew of liquid compost. Mr Tea’s recipe is as good as any batch of Biodynamic Preps or EM (Effective Micro-organisms) you might already be using. It is inestimably superior to MiracleGrow® or other commercial, bagged soil amendments.
In a large stainless steel tank retrofitted with aerating pipes, Mr Tea combines de-chlorinated warm water and…
- Folic Acid
- Fish Oil Emulsion
- Bat Guano
- Feather Meal
- Virgin Forest Soil
- Deep Pasture Topsoil
- Composted Animal Manure
- Composted Kitchen Scraps
- Composted Poultry Litter
- Worm Castings & Liquor, and
The kelp, fish oil, and most of the composts provide rich food for the microbes while they brew. The humates are million-year old deposits with diverse paleobacteria. The bat guano is drawn from distant caves rich in trace minerals and packed with still more varieties of exotic bacteria. The two kinds of soil contain a complex of two discrete living microbiomes, one the fungally-rich virgin forest and the other a bacterially dominated grasslands. The fine biochar particulates provide enough soil structure to retain water – about 10 times the volume of the biochar itself — and aerobic conditions, while providing a coral reef-like microbial habitat. The animal manures, worm castings, feather meal and compostables all contribute to the biodiversity of available microfauna.
In the world of bacterial epigenetics, dictated by the particular demands of diverse members of the web in different seasons and weather conditions, this is a supermarket of genotypes that allow the bacteria to switch up and morph into whatever might be needed for soil health and fertility, capturing passing genes and unlocking regions of their DNA and RNA to provide new or ancient solutions to current conditions.
Bandwidth permitting, you can watch this video that's so sexy it should be x-rated. This is a revolution disguised as organic gardening. The sex is going on right in front of the camera, you’d just need a microscope to see it. Use your imagination.
If we want to stop global climate change while still surviving unpredictable and changing weather patterns, we’ll need to hold more water, nutrients and carbon in the soil. We can do that with a good diversity of healthy microorganisms and their byproducts.
We're trying to increase the retention time of carbon in its solid form in the land for as long as possible, as opposed to allowing it to become gaseous, because that's when it becomes dangerous to our future.
That is what climate farming, or what my friend Darren Doherty calls regrarianism, is all about. Its about improving the soil to heal the atmosphere.
As we say in the clip, this is agriculture that builds rather than mines the soil and can transform our beloved home back into a garden planet.


With the University of Michigan’s latest production of a quantum chip, it’s another step forward for quantum computers that will someday dwarf the abilities of today’s machines.
Working with individual ions or atoms – much smaller than the transistors of even the most advanced microchips - quantum computers may be both more powerful and more compact than existing computers by various orders of magnitude.
Common computers today are thousands of times more powerful and more compact than the first 30 ton behemoths, but they use virtually the same logic. The fundamental design has gone unchanged for 50 years.
Quantum computing is whole new ball game. The secret lies in the almost magical property of quantum matter to adopt two states simultaneously. Normal integrated circuits store data using transistors which have just two states – on and off. Each quantum circuit, or qubit, can represent at least three states: on, off or both by an effect called quantum superposition. This means much more data can be stored on each individual circuit.
Actually, qubits can potentially contain many states. Dr Andrew White, Senior Lecturer in Physics at University of Queensland describes a qubit like this: “A quantum computer takes that on or off state and adds many different possible states. The first thing, if you think of the globe, let the South Pole be on, the North Pole off – that’s not a very good description of the globe. A quantum computer let’s you describe information by saying, look, you can take an arrow from Earth’s center and point it at the North Pole, South Pole or Los Angeles or London, and that’s richer description. You can fit much more information on a single qubit.”
Based on Dr. White’s description, a single qubit could replace a whole bank of conventional memory. Normal memory holds a large array of binary numbers expressed as on or off transistors – ones or zeros. Many transistors are needed to express anything more than just a simple number – hence today’s computers need for large memories. For example: you need 8 bits plus one bit for error correction to store the binary number for 256 which is expressed as 11111111. Going back to our globe example, our arrow could point to Amsterdam which could represent 256 – or any other number. A single qubit could store more information than thousands of transistors.
This compact storage leads to another advantage: speed. Without the need to access many memory locations to read data, retrieval is almost instantaneous.
Quantum computers will represent a huge leap in processing power as well – they could execute instructions exponentially faster because there would be almost no limit to the size of the instruction. Currently, most computers use 32 or 64 bit instructions.
There is another exciting benefit to working with quantum reactions: Entanglement. It describes the ability of quantum matter to “link” two particles. Change one particle and the other changes – instantaneously, even though there is no physical connection! And distance may be irrelevant! This property – not fully understood – would enable computers to talk to each other with no time lag over long distances.
Anton Zeilinger at the Institute of Experimental Physics in Vienna, Austria, preformed an experiment to demonstrate entanglement: their group strung an optical-fiber cable in a sewer tunnel under the Danube River with an "entangled" photon at each end. They measured of the state of polarization in one photon (horizontal, vertical, etc…) establishing that the other proton immediately had an identical polarization.
What will be the difference to normal computer users? Try instant access to any type of data – whether it is in your computer or on the other side of the planet. As for processing power, few users rarely exceed the abilities of today’s computers. Much computer hardware is used to generate the fancy graphical interface we call Windows – with plenty left over in reserve.
Those not familiar with computer science are often surprised to learn there are still a few applications that cannot run easily on today’s computers. They lack of sufficient processing power to do climate modeling, artificial intelligence or break strong encryption.
The NSA (National Security Agency) would love to be able to break many a foreign power’s encrypted communications, but has been stymied by the lack of a sufficiently fast computer for the job. Experts estimate it would take more than the lifetime of the Universe using all the computers in the world to break a 1024 bit encryption key – the current standard for serious encryption applications. It’s worth noting that most commercial encryption only uses a 40 bit key. A quantum computer has the potential to break any encryption in a few days.
Scientists who study global warming and climate would like to have finer-grained models to be able to predict the weather more effectively and determine the real impact man’s activities have over the planet. Current computers, although fast, still take hours or days to produce weather simulations that lack detail.
Artificial intelligence is another field that could use the extra processing power. Current algorithms simply can’t be processed fast enough and, admittedly, may need more refining. However, a quantum computer could theoretically contain more processing power than the human brain in a smaller space – making true AI possible.
In fact, more powerful computers often come along well before a use is found for them. In the future, more uses will be found for quantum machines as their tremendous processing power becomes available.
But having the machine is not enough. All of today’s software is based on the silicon technology it runs on. New software is already being written to take advantage of quantum computation.
One of the most important steps is to write software for error checking. All computers use some type of system to make sure a bit hasn’t accidentally “flopped” from a one to a zero. Quantum computer components, because of their atomic size, will be very susceptible to errors. In fact, one of the biggest problems faced by the scientists working on quantum computing is the problem associated with checking the state of an object so small. How does one check the value of a qubit without changing it? Error checking will be of critical importance and computer scientists have already developed some ideas to insure accuracy in quantum systems.
They have also already developed algorithms and equipment for super strong quantum encryption designed to allow hacker-proof security for communications. The National Security Agency and Federal Reserve banks can now buy a quantum cryptographic system from several companies. Anyone who intercepts and tries to read the stream of photons used will disturb the photons in a way that is detectable to both sender and receiver.
Quantum encryption represents the first major commercial implementation for what has become known as quantum information science - a blending of quantum mechanics and information theory.
As for the software you use in day-to-day computing, no changes will be necessary. Just as software emulators permit Apple users to run Windows and Windows software on the Mac’s Power PC processor – albeit sacrificing some speed – an emulator could quite easily run any programs today at speeds that make the today’s fastest processors look frozen. So you won’t need to run out and buy Microsoft Office 2030 for Quantum Computers – although Bill Gates, if he’s still alive, might like that.
It may also change the way we do computing. Like times past when computers were very expensive, we may share a large, centralized quantum computer – one that has the capacity to handle quadrillions of transactions. Connections would be via fiber optic connections and personal data – a whole lifetimes worth – could be stored on a quantum USB-type memory the size of a credit card. This would eliminate the need to have millions of PCs that require upgrading every few years.
Don’t expect any of this to happen tomorrow. Scientists are still struggling with some tough problems. Which is the best material from which to make quantum systems? How to check qubit values and not lose the information at the same time? What mechanisms are involved in entanglement? Some experts predict it will be 20 years before we see the first fully functional computers that use quantum materials.
No mater how long it takes, money will continue to flow into research efforts. Silicon-based processors are beginning to near the physical limit of smallness and speed. Intel’s best processors currently fabricated using .15 micron process and run 3GHZ.
One day we may have more processing power than we know what to do with. It will be up to our imaginations – something no computer may ever accurately match - to think of new problems for these enormously powerful machines to solve.
by Philip Dunn, Copyright 2005 PhysOrg.com
Explore further: Superfast fluorescence sets new speed record


Quantum teleportation, or entanglement-assisted teleportation, is a technique used to transfer quantum information from one quantum system to another. It does not transport the system itself, nor does it allow communication of information at superluminal (faster than light) speed. Neither does it concern rearranging the particles of a macroscopic object to copy the form of another object. Its distinguishing feature is that it can transmit the information present in a quantum superposition, useful for quantum communication and computation.
More precisely, quantum teleportation is a quantum protocol by which a qubit a (the basic unit of quantum information) can be transmitted exactly (in principle) from one location to another. The prerequisites are a conventional communication channel capable of transmitting two classical bits (i.e. one of four states), and an entangled pair (b,c) of qubits, with b at the origin and c at the destination. (So whereas b and c are intimately related, a is entirely independent of them other than being initially colocated with b.) The protocol has three steps: measure a and b jointly to yield two classical bits; transmit the two bits to the other end of the channel (the only potentially time-consuming step, due to speed-of-light considerations); and use the two bits to select one of four ways of recovering c. The upshot of this protocol is to permute the original arrangement ((a,b),c) to ((b′,c′),a), that is, a moves to where c was and the previously separated qubits of the Bell pair turn into a new Bell pair (b′,c′) at the origin.
Suppose Alice has a qubit in some arbitrary quantum state . (A qubit may be represented as a superposition of states, labeled and .) Assume that this quantum state is not known to Alice and she would like to send this state to Bob. Ostensibly, Alice has the following options:
Option 1 is highly undesirable because quantum states are fragile and any perturbation en route would corrupt the state.
Option 2 is forbidden by the no-broadcast theorem.
Option 3 (classical teleportation) has also been formally shown to be impossible. (See the no teleportation theorem.) This is another way to say that quantum information cannot be measured reliably.
Thus, Alice seems to face an impossible problem. A solution was discovered by Bennett, et al. The components of a maximally entangled two-qubit state are distributed to Alice and Bob. The protocol then involves Alice and Bob interacting locally with the qubit(s) in their possession and Alice sending two classical bits to Bob. In the end, the qubit in Bob's possession will be in the desired state.
Assume that Alice and Bob share an entangled qubit AB. That is, Alice has one half, A, and Bob has the other half, B. Let C denote the qubit Alice wishes to transmit to Bob.
Alice applies a unitary operation on the qubits AC and measures the result to obtain two classical bits. In this process, the two qubits are destroyed. Bob's qubit, B, now contains information about C; however, the information is somewhat randomized. More specifically, Bob's qubit B is in one of four states uniformly chosen at random and Bob cannot obtain any information about C from his qubit.
Alice provides her two measured classical bits, which indicate which of the four states Bob possesses. Bob applies a unitary transformation which depends on the classical bits he obtains from Alice, transforming his qubit into an identical re-creation of the qubit C.
Suppose Alice has a qubit that she wants to teleport to Bob. This qubit can be written generally as:
Alice takes one of the particles in the pair, and Bob keeps the other one. The subscripts A and B in the entangled state refer to Alice's or Bob's particle. We will assume that Alice and Bob share the entangled state .
So, Alice has two particles (C, the one she wants to teleport, and A, one of the entangled pair), and Bob has one particle, B. In the total system, the state of these three particles is given by
Alice will then make a partial measurement in the Bell basis on the two qubits in her possession. To make the result of her measurement clear, we will rewrite the two qubits of Alice in the Bell basis via the following general identities (these can be easily verified):
The three particle state shown above thus becomes the following four-term superposition:
Notice all we have done so far is a change of basis on Alice's part of the system. No operation has been performed and the three particles are still in the same state. The actual teleportation starts when Alice measures her two qubits in the Bell basis. Given the above expression, evidently the result of her (local) measurement is that the three-particle state would collapse to one of the following four states (with equal probability of obtaining each):
Alice's two particles are now entangled to each other, in one of the four Bell states. The entanglement originally shared between Alice's and Bob's is now broken. Bob's particle takes on one of the four superposition states shown above. Note how Bob's qubit is now in a state that resembles the state to be teleported. The four possible states for Bob's qubit are unitary images of the state to be teleported.
The crucial step, the local measurement done by Alice on the Bell basis, is done. It is clear how to proceed further. Alice now has complete knowledge of the state of the three particles; the result of her Bell measurement tells her which of the four states the system is in. She simply has to send her results to Bob through a classical channel. Two classical bits can communicate which of the four results she obtained.
After Bob receives the message from Alice, he will know which of the four states his particle is in. Using this information, he performs a unitary operation on his particle to transform it to the desired state :
to recover the state.
to his qubit.
Teleportation is therefore achieved.
Experimentally, the projective measurement done by Alice may be achieved via a series of laser pulses directed at the two particles.
In the literature, one might find alternative, but completely equivalent, descriptions of the teleportation protocol given above. Namely, the unitary transformation that is the change of basis (from the standard product basis into the Bell basis) can also be implemented by quantum gates. Direct calculation shows that this gate is given by
Entanglement can be applied not just to pure states, but also mixed states, or even the undefined state of an entangled particle. The so-called entanglement swapping is a simple and illustrative example.
If Alice has a particle which is entangled with a particle owned by Bob, and Bob teleports it to Carol, then afterwards, Alice's particle is entangled with Carol's.
A more symmetric way to describe the situation is the following: Alice has one particle, Bob two, and Carol one. Alice's particle and Bob's first particle are entangled, and so are Bob's second and Carol's particle:
___ / \ Alice-:-:-:-:-:-Bob1 -:- Bob2-:-:-:-:-:-Carol \___/
Now, if Bob performs a projective measurement on his two particles in the Bell state basis and communicates the results to Carol, as per the teleportation scheme described above, the state of Bob's first particle can be teleported to Carol's. Although Alice and Carol never interacted with each other, their particles are now entangled.
One can imagine how the teleportation scheme given above might be extended to N-state particles, i.e. particles whose states lie in the N dimensional Hilbert space. The combined system of the three particles now has a N3 dimensional state space. To teleport, Alice makes a partial measurement on the two particles in her possession in some entangled basis on the N2 dimensional subsystem. This measurement has N2 equally probable outcomes, which are then communicated to Bob classically. Bob recovers the desired state by sending his particle through an appropriate unitary gate.
A general teleportation scheme can be described as follows. Three quantum systems are involved. System 1 is the (unknown) state ρ to be teleported by Alice. Systems 2 and 3 are in a maximally entangled state ω that are distributed to Alice and Bob, respectively. The total system is then in the state
where Tr12 is the partial trace operation with respect systems 1 and 2, and denotes the composition of maps. This describes the channel in the Schrödinger picture.
Taking adjoint maps in the Heisenberg picture, the success condition becomes
for all observable O on Bob's system. The tensor factor in is while that of is .
The proposed channel Φ can be described more explicitly. To begin teleportation, Alice performs a local measurement on the two subsystems (1 and 2) in her possession. Assume the local measurement have effects
If the measurement registers the i-th outcome, the overall state collapses to
The tensor factor in is while that of is . Bob then applies a corresponding local operation Ψi on system 3. On the combined system, this is described by
where Id is the identity map on the composite system .
Therefore the channel Φ is defined by
Notice Φ satisfies the definition of LOCC. As stated above, the teleportation is said to be successful if, for all observable O on Bob's system, the equality
holds. The left hand side of the equation is:
where Ψi* is the adjoint of Ψi in the Heisenberg picture. Assuming all objects are finite dimensional, this becomes
The success criterion for teleportation has the expression


Photonic chips go 3D
Technology Research News
The dream of building computer chips that
use light signals rather than electricity has entered the realm of serious
research in recent years with the advent of photonic crystal, a material
that blocks and channels light within extremely small spaces.
Producing practical photonic crystal chips, however, includes
several challenges: making three-dimensional devices that emit light from
specific points, emit at the wavelengths used by today's optical telecommunications
equipment and can be manufactured using processes suited to mass production.
Research teams from the Massachusetts Institute of Technology
and from Kyoto University have made devices that meet all three challenges.
The techniques could be used to make smaller, more efficient communications
devices; create optical memory and quantum computing and communications
devices; develop new types of lasers and biological and chemical sensors;
and could ultimately lead to all-optical computer processors.
The semiconductor industry took off with the advent of a practical
and low-cost method of integrating a large number of transistors into
a single chip, said Minghao Qi, a research assistant at MIT. "It is natural
then to envision the possibility of integrated photonics, where information
is processed fully in the optical domain [at the high] bandwidth of photons,"
Photonic crystal is usually made from the same semiconductor materials
as computer chips using common chipmaking techniques like photolithography.
It contains regularly spaced gaps of air or other materials that form
boundaries within the crystal that refract, or bend, specific wavelengths
of light. Refraction is responsible for the illusion that a drinking straw
bends at the air-liquid boundary. Portions of the materials that do not
contain gaps channel light within the crystal and emit light from it.
The MIT photonic chip has seven layers that each contain two types
of two-dimensional photonic crystal. One type is an arrangement of rods
surrounded by air and the other type is solid material perforated with
air holes. The rod slab is positioned above the hole slab in each layer,
and the layers are offset to produce steps. The holes are about 500 nanometers
in diameter, or about one-tenth the size of a red blood cell. The material
blocks light at wavelengths of 1.3, 1.4 and 1.5 microns. Telecommunications
systems use near-infrared 1.3- and 1.55-micron wavelengths.
The researchers filled specific air holes and gaps between rods
during the manufacturing process to create solid areas, or defects, that
emit light. "A critical goal in photonic crystal [research] is the ability
to put arbitrary defects with precisely controlled shapes and sizes at
designed locations," said Qi.
The two types of two-dimensional photonic crystal in each layer
of the three-dimensional crystal also allow for polarization control,
said Qi. A light beam's electric field is ordinarily oriented in a plane
perpendicular to the beam. The electric field of polarized light is confined
to one direction within the plane. Controlling polarization is important
because transferring light signals from photonic crystal to optical fibers
requires matching the polarizations of the devices, he said.
The crystal is more efficient than previous three-dimensional
photonic crystals, and the seven layers can be formed in four processing
steps, said Qi.
The Kyoto University team has advanced its existing woodpile-structured
three-dimensional photonic crystal with a method to make solid areas in
specific locations and have shown that the material precisely controlled
light, said Susumu Noda, a professor of electronic science and engineering
at Kyoto University.
The woodpile photonic crystal consists of perpendicular layers
of semiconductor rods. The researchers' design calls for 200-nanometer-wide
rods spaced 700 nanometers center to center. The photonic crystal controls
The researchers also sandwiched a light source inside their photonic
crystal, which is a step toward fully integrated optical devices, said
The MIT process could be used to make practical telecommunications
devices and biological and chemical sensors in two to three years, said
Qi. High-quality devices that could be coupled to optical fiber could
take five years, he said. Simple all-optical computer chips could take
10 years to develop, he said.
Devices based on the Kyoto method could become practical in five
to ten years, said Susumu.
Qi's research colleagues were Elefterios Lidorikis, Peter Rakich,
Stephen Johnson, John Joannopoulos, Erich Ippen and Henry Smith. The work
appeared in the June 3, 2004 issue of Nature. The research was
funded by the National Science Foundation (NSF).
Susumu's research colleagues were Shinpei Ogawa, Masahiro Imada,
Susumu Yoshimoto and Makoto Okano. The work appeared in the June 3, 2004
issue of Sciencexpress. The research was funded by Core Research
for Evolution Science and Technology (CREST), Japan Science and Technology
Agency (JST), and the Ministry of Education, Culture, Sports, Science
and Technology (MEXT) of Japan.
Timeline: 2-3 years, 5 years, 7-8 years,
Funding: Government, Corporate
TRN Categories: Optical Computing, Optoelectronics and Photonics;
Materials Science and Engineering
Story Type: News
Related Elements: Technical paper, "Control of Light Emission
by 3D Photonic Crystals", Sciencexpress, June 3, 2004; technical paper,
"A Three-dimensional Optical Photonic Crystal with Design Point Defects,"
Nature, June 3, 2004
July 28/August 4, 2004
Photonic chips go 3D
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Electric fields assemble
silicon on plastic
fast laser tweezer
chains make quantum wires
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RSA was first described in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman of the Massachusetts Institute of Technology. Public-key cryptography, also known as asymmetric cryptography, uses two different but mathematically linked keys, one public and one private. The public key can be shared with everyone, whereas the private key must be kept secret. In RSA cryptography, both the public and the private keys can encrypt a message; the opposite key from the one used to encrypt a message is used to decrypt it. This attribute is one reason why RSA has become the most widely used asymmetric algorithm: It provides a method of assuring the confidentiality, integrity, authenticity and non-reputability of electronic communications and data storage.
Many protocols like SSH, OpenPGP, S/MIME, and SSL/TLS rely on RSA for encryption and digital signature functions. It is also used in software programs -- browsers are an obvious example, which need to establish a secure connection over an insecure network like the Internet or validate a digital signature. RSA signature verification is one of the most commonly performed operations in IT.
Explaining RSA's popularity
RSA derives its security from the difficulty of factoring large integers that are the product of two large prime numbers. Multiplying these two numbers is easy, but determining the original prime numbers from the total -- factoring -- is considered infeasible due to the time it would take even using today’s super computers.
The public and the private key-generation algorithm is the most complex part of RSA cryptography. Two large prime numbers, p and q, are generated using the Rabin-Miller primality test algorithm. A modulus n is calculated by multiplying p and q. This number is used by both the public and private keys and provides the link between them. Its length, usually expressed in bits, is called the key length. The public key consists of the modulus n, and a public exponent, e, which is normally set at 65537, as it's a prime number that is not too large. The e figure doesn't have to be a secretly selected prime number as the public key is shared with everyone. The private key consists of the modulus n and the private exponent d, which is calculated using the Extended Euclidean algorithm to find the multiplicative inverse with respect to the totient of n.
A simple, worked example
Alice generates her RSA keys by selecting two primes: p=11 and q=13. The modulus n=p×q=143. The totient of n ϕ(n)=(p−1)x(q−1)=120. She chooses 7 for her RSA public key e and calculates her RSA private key using the Extended Euclidean Algorithm which gives her 103.
Bob wants to send Alice an encrypted message M so he obtains her RSA public key (n, e) which in this example is (143, 7). His plaintext message is just the number 9 and is encrypted into ciphertext C as follows:
Me mod n = 97 mod 143 = 48 = C
When Alice receives Bob’s message she decrypts it by using her RSA private key (d, n) as follows:
Cd mod n = 48103 mod 143 = 9 = M
To use RSA keys to digitally sign a message, Alice would create a hash or message digest of her message to Bob, encrypt the hash value with her RSA private key and add it to the message. Bob can then verify that the message has been sent by Alice and has not been altered by decrypting the hash value with her public key. If this value matches the hash of the original message, then only Alice could have sent it (authentication and non-repudiation) and the message is exactly as she wrote it (integrity). Alice could, of course, encrypt her message with Bob’s RSA public key (confidentiality) before sending it to Bob. A digital certificate contains information that identifies the certificate's owner and also contains the owner's public key. Certificates are signed by the certificate authority that issues them, and can simplify the process of obtaining public keys and verifying the owner.
Security of RSA
As discussed, the security of RSA relies on the computational difficulty of factoring large integers. As computing power increases and more efficient factoring algorithms are discovered, the ability to factor larger and larger numbers also increases. Encryption strength is directly tied to key size, and doubling key length delivers an exponential increase in strength, although it does impair performance. RSA keys are typically 1024- or 2048-bits long, but experts believe that 1024-bit keys could be broken in the near future, which is why government and industry are moving to a minimum key length of 2048-bits. Barring an unforeseen breakthrough in quantum computing, it should be many years before longer keys are required, but elliptic curve cryptography is gaining favor with many security experts as an alternative to RSA for implementing public-key cryptography. It can create faster, smaller and more efficient cryptographic keys. Much of today’s hardware and software is ECC-ready and its popularity is likely to grow as it can deliver equivalent security with lower computing power and battery resource usage, making it more suitable for mobile apps than RSA. Finally, a team of researchers which included Adi Shamir, a co-inventor of RSA, has successfully determined a 4096-bit RSA key using acoustic cryptanalysis, however any encryption algorithm is vulnerable to this type of attack.
The inventors of the RSA algorithm founded RSA Data Security in 1983. The company was later acquired by Security Dynamics, which was in turn purchased by EMC Corporation in 2006. The RSA algorithm was released to the public domain by RSA Security in 2000.
Continue Reading About RSA algorithm (Rivest-Shamir-Adleman)
Margaret Rouse asks:
Given the various stories linking RSA Security to the NSA’s attempts to weaken encryption products and subvert cryptography standards, how much faith do you have in the RSA cryptosystem and today’s popular encryption algorithms?
1 ResponseJoin the Discussion


String theory was originally developed to try and describe the fundamental particles and forces that make up our universe. Over the last 25 years, string theory has become some physicists' contender for a 'theory of everything', reconciling particle physics with cosmology - a puzzle that tormented Einstein for the last 30 years of his life.
It contends that the subatomic particles found in nature, such as electrons and quarks, may not be particles at all but instead tiny vibrating strings. String theorists said our universe is 10-dimensional but during the big bang, 6 of those 10 dimensions curled up into a tiny ball and the remaining '4' (they count time as a dimension even though it relies on the other three dimensions) expanded explosively, providing us with the universe we know and love, including the cast of "Jersey Shore".
How did these six dimensions compactify? There's no mathematical basis for topology and properties of these higher-dimensional universes. Where do strings come from? No one knew so what we ended up with were multiple 'string theories', which means it stands a chance of not being a theory at all. Some even proposed M-theory (11-dimensions) to get away from focusing on strings entirely.(1)
There's no shortage of instances where theory, deduction or inference have survived being falsifiable just fine and later been proven to be correct but in a modern science world a half dozen 'theories of a theory' won't get much traction outside people who want funding.
An upcoming article in Physical Review Letters says it can change all that and make string theory experimental. Their reasoning? They say string theory seems to predict the behavior of entangled quantum particles and since that prediction can be tested in the laboratory, they can now test string theory - predicting how entangled quantum particles behave provides the first opportunity to test string theory by experiment because quantum entanglement can be measured in the lab.(2)
There is no obvious connection to explain why a theory that is being developed to describe the fundamental workings of our universe is useful for predicting the behavior of entangled quantum systems but if it checks out, it will be an interesting insight.
"This will not be proof that string theory is the right 'theory of everything' that is being sought by cosmologists and particle physicists. However, it will be very important to theoreticians because it will demonstrate whether or not string theory works, even if its application is in an unexpected and unrelated area of physics," says professor Mike Duff, lead author of the study from the Department of Theoretical Physics at Imperial College London. "If experiments prove that our predictions about quantum entanglement are correct, this will demonstrate that string theory 'works' to predict the behaviour of entangled quantum systems.
"This may be telling us something very deep about the world we live in, or it may be no more than a quirky coincidence. Either way, it's useful."
Article: M. J. Duff , L. Borsten, D. Dahanayke , W. Rubens, A. Marrani, 'Four-qubit entanglement from string theory', arXiv:1005.4915v2 and Physical Review Letters 2010 (in press)
(1) String theory
String theory, and its extension M-theory, are mathematical descriptions of the universe. They have been developed, over the last 25 years, by theoreticians seeking to reconcile the theories of general relativity and quantum mechanics. (The former describes the universe at the level of cosmology – the very large, while the latter describes the universe at the level of particle physics – the incredibly small). One of the major bugbears, especially of M-theory, is that it describes billions of different universes and ‘anything’ can be accommodated in one or other of the M-theory universes. Researchers have no way of testing which of the answers that string/M-theory gives us is ‘right’. Indeed, they all may be right and we live in one universe among an infinite number of universes. So far no one has been able to make a prediction, using string theory, that can be tested to see if it is correct or not.
(2) Qubit (quantum bit) entanglement
Under very precisely controlled conditions it is possible to entangle the properties of two quantum particles (two quantum bits, or qubits), for example two photons. If you then measure the state of one of these entangled particles, you immediately affect the state of its partner. And this is true if the particles are close to one another or separated by enormous distance. Hence Einstein’s apposite description of quantum entanglement as ‘spooky action at a distance’. It is possible to entangle more than two qubits, but calculating how the particles are entangled with one another becomes increasingly complex as more particles are included.
Duff and colleagues say they realized that the mathematical description of the pattern of entanglement between three qubits resembles the mathematical description, in string theory, of a particular class of black holes. Thus, by combining their knowledge of two of the strangest phenomena in the universe, black holes and quantum entanglement, they realized they could use string theory to produce a prediction that could be tested. Using the string theory mathematics that describes black holes, they predicted the pattern of entanglement that will occur when four qubits are entangled with one another. (The answer to this problem has not been calculated before.) Although it is technically difficult to do, the pattern of entanglement between four entangled qubits could be measured in the laboratory and the accuracy of this prediction tested.
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SAN JOSE, Calif. IBM's Almaden Research Center unveiled the world's largest quantum computer to date a 5-bit computer squeezed onto a single molecule at the Hot Chips conference last week. The five fluorine atoms in the molecule each represent a quantum bit, or "qubit," which made the computer the first ever capable of solving a problem related to code cracking, called the order-finding problem, in a single step.
"Every other computer in the world takes several steps to solve the order-finding problem, but our quantum computer solved it in a single step," said Stanford University researcher Lieven Vandersypen. The quantum computer was invented by IBM Almaden Research Center researcher Isaac Chuang, who led a team of scientists that included fellow researchers Gregory Breyta and Costantino Yannoni of IBM Almaden, professor Richard Cleve of the University of Calgary, and researchers Matthias Steffen and Lieven Vandersypen from Stanford University.
Long way to go
Since the late 1980s Chuang has been pursuing ever-more-sophisticated realizations of quantum computers. His last effort was a 3-qubit machine. While the latest version represents a rapid advance for the field, quantum computing still has a long way to go before it will compete with leading-edge supercomputers. But researchers in the field are optimistic that machines of competitive size will appear in this decade.
That optimism was reflected in a statement by IBM's Chuang. "This result gives us a great deal of confidence in understanding how quantum computing can evolve into a future technology," Chuang said. "It reinforces the growing realization that quantum computers may someday be able to live up to their potential of solving, in remarkably short times, problems that are so complex that the most powerful supercomputers couldn't calculate the answers even if they worked on them for millions of years."
The order-finding problem determines the period of a function. In digital computers, that requires a step-by-step iterative solution of the function's values until they begin to repeat. The quantum computer, however, solved the order-finding problem without any iteration steps.
Its ability to obtain a single-step solution can be traced to the nature of qubits. Because quantum bits simultaneously represent all possible values of the input variables, the single step of a quantum computer considers every possible input value at once. Hence, the single step can solve problems of any size. That represents the ultimate in parallel processing: parallelism at the bit level.
While a quantum computation starts and ends with information encoded in binary bits, the computation itself is performed in the mysterious realm of quantum mechanics, where a physical system can be in what is known as a superposition of states.
Using nuclear magnetic resonance, it is possible to measure whether the constituent particles of an atom the protons and neutrons in its nucleus are spinning in one direction or another. Such a measurement represents the output stage of the computation, since once observed, an elementary particle's spin becomes fixed in one of its binary states: spin up or spin down.
One spin direction is designated "0" and the other designated "1," but both are only probabilities during the course of a computation. IBM's 5-bit quantum computer used the spin configuration in fluorine atoms to represent qubits, but other experiments have employed the spin of carbon or oxygen atoms.
Logic is performed in any quantum computer when its qubit atoms affect the spin of neighboring qubit atoms. When structured properly, the quantum-computer atom can perform a number of mathematical operations in parallel.
In short, quantum operations are the reversible generalizations of standard digital operations. A quantum computer's basic operations are often compared with probabalistic algorithms.
Many probabalistic algorithms can be sped up by random search methods. For instance, the occasional multiplying of intermediate results by a random number and checking for performance gains can uncover shortcuts in gradient descent algorithms that would otherwise have to be discovered one by one via exhaustive searches. Such probabalistic circuits can always be transformed into larger, slower deterministic circuits.
For the two-element order-finding problem here, a deterministic circuit requires an exponential number of steps (four), while a probabalistic circuit only requires a polynomial number of steps (less than four, but more than one). The quantum circuit required only a single step.
Quantum circuits extend the probabilistic notion by generalizing the one-way operations of both deterministic and probabilistic operations into reversible operations. Qubits enable reversible procedures by taking on not only the 1 and 0 symbolized by all bits but also holding a vector length expressed as a complex number. Thus, a qubit encodes both a spin direction expressed as 1 or 0 and a complex amplitude.
The resulting qubit vector is angled into a multidimensional space equal in dimension to the number of qubits stored in a system. A 2-bit qubit computer thus can solve, in a single step, problems represented in two-dimensional space. In IBM's 5-qubit quantum computer, only two qubits could be used, since three had to be reserved for calculating the result. Consequently, IBM's 5-qubit quantum computer was only able to solve 2-bit problems. However, future multibit quantum computers should in theory scale up to higher dimensional spaces merely by adding qubits.
The biggest problem with quantum computers is that the quantum states must remain unobserved, or "decoherence" will spoil their ability to take on different values simultaneously and therefore disable them from solving problems in a single step. That problem stymied the first attempts to build quantum computers, since any isolated particle, such as an electron or photon, could be too easily disturbed by environmental effects. The first successes at Harvard, MIT and IBM's Almaden Research Center were based on the use of atoms as stable environments for particle states.
IBM's answer here, suggested earlier this year in a paper by Cleve, was to tack on a quantum Fourier transform of the results and then decode the answer from its spectrum. A quantum Fourier transform essentially performs a discrete Fourier transform on the amplitude part of the qubit vector, allowing the final quantum state of the computer to be inferred by humans after their examination of the qubit atom's frequency spectrum, rather than through direct observation of the probabilistic state.
The specific problem IBM's 5-qubit computer tackled was the ordering problem, a precursor to the integer-factoring algorithm used to decode encyphered data. Traditional deterministic algorithms must exponentially expand computing resources as problems get bigger, but with a quantum computer it takes the same number of steps to solve any size problem, as long as there are enough qubits to encode the variables and the algorithm. Thus, the CPU's power scales up exponentially with the number of bits in its "registers."
That fact, and a practical quantum-based algorithm for factoring large numbers, was first published in 1994 by Peter Shor of AT&T Research. Since encryption plays a central role in national security, Shor's result stimulated a round of government funding in quantum-computer research.
Two bits, four ways
The order-finding problem used in IBM's demonstration essentially found the period of a 2-bit function. Here, that amounted to repeatedly permuting a 2-bit string with the same function four possible ways for two bits until returning to the original 2-bit value. The number of permutations needed is equal to the period of the "ordering" function. According to a statement by IBM, this is the most complex algorithm yet solved by an actual quantum computer.
For the five-qubit quantum computer, a two-element ordering problem was encoded by putting the starting state in the first two qubits. Radio frequency pulses were used to put the five atoms into the correct starting state, then a second set of pulses induced a single permutation of the function in the two "input atoms," and the interactions among the spins caused the answer to be calculated.
"In essence, the quantum computer simultaneously answers what happens after one, two, three and four permutations; then we take the quantum Fourier transform to find the period," said Vandersypen. The quantum Fourier transform was measured with standard laboratory magnetic resonance equipment, permitting the results to be read out from the spectrum of three qubit atoms.
Once these molecular methods mature, they may actually represent an advance over silicon-circuit fabrication processes. Instead of having to define complex circuits from the ground up using photographically reduced drawings, quantum circuits could be fabricated using automatic controlled chemical reactions. Current research indicates that the use of internal nuclear states is a stable environment for the representation and modification of qubits.


Story 2 - 22/10/2012
A Wind Tunnel
Simulating quantum phenomena on today’s computers can be extremely challenging. Yet, just like the wind tunnel changed the trajectory of modern aviation, new specially built quantum simulators may soon guide the design of tailor-made quantum materials.
for Quantum Physics
Now also in Spanish
Inside the quantum wind tunnel. The individual ions (dots) behave like tiny magnet bars (spins) which can orient themselves according to their neighbors and reproduce very complex quantum phenomena.
Un túnel de viento para la física cuántica
Um túnel de vento para a física quântica,
brought to you by
Optics and Photonics Latin America
In the early days of aeronautics, computers that could simulate the subtle laws of aerodynamics did not exist. For this reason, people built wind tunnels to study the physics of flight on model systems. Quantum physicists are now facing a similar situation where they cannot satisfactorily simulate the behavior of many interesting quantum systems on even the most powerful computers. Scientists have, therefore, been looking for ways to build some physical systems that may be used as quantum simulators
, the quantum analog of wind tunnels. This has so far been possible only for relatively simple quantum systems, involving only a few dozens of interacting quantum particles. However, many interesting effects are believed to happen in the presence of a larger number of interacting particles. Joe Britton, at the National Institute of Standards and Technology (NIST) in Boulder, Colorado, USA, and coworkers have now demonstrated rudimentary operation of a quantum simulator with hundreds of simultaneously interacting quantum particles. The NIST machine may well be a stepping-stone on our way towards a rational design of quantum materials.
Why simulate? After all, the laws of aerodynamics and quantum physics can be described using mathematical laws. Interestingly, however, these laws lead to very subtle and complex phenomena. On the one hand, air flowing around the wing of an aircraft, for example, frequently leads to rather strong turbulence. On the other hand, interacting quantum particles can depend on each other without exchanging any signals. Both situations can
be described mathematically. At the same time, however, they are excruciatingly difficult
to reproduce with computer simulations. The turbulent flow of air is a chaotic phenomenon for which tiny inaccuracies of the computer simulation can potentially lead to totally wrong predictions. Interacting quantum particles have many degrees of freedom, and this easily brings even today’s largest supercomputers to their knees.
Wind tunnels and quantum simulators are used to reproduce
a phenomenon directly in a controlled environment. Instead of mathematically describing the air particles, they use real air streams; instead of writing mathematical models of quantum particles, they use quantum systems such as ions to actually produce an interesting effect. And the wind tunnel or simulator allows the experimenters to easily modify experimental conditions such as wind speeds or interaction strengths.
What questions can be answered using these tools? The history of aviation may give us some hints: in the early 1900s even the slightest glitch in the design of an airplane or parachute would often mean the certain death of the pilot. Yet, in order to advance the times’ understanding of aerodynamics, it was essential to identify what aspects of avian flight were generating the lift: was it the movement
of their wings? The shape
of their wings? Or their material
? And how could artificial wings that generated enough lift to make humans fly be built? To answer these questions, the Wright brothers and many of their peers studied smaller scale models in very basic wind tunnels. After all, these experiments were far less deadly than jumping off cliffs. And after countless attempts and fails, people had enough knowledge and ingenuity to build the first airplanes.
Today’s quantum science and engineering are not dissimilar to the science and engineering of early aviation: how can we sustain
specific quantum phenomena? How can we suppress
unwanted interference and interaction between our quantum system and the uncontrolled environment?
The main reason for the complexity of quantum physics is quantum superposition and entanglement  – arguably the most striking difference between classical and quantum physics. A classical binary digit (bit) can represent either the number 0 or the number 1. Therefore, to describe N bits, only N numbers are required. This binary language is the foundation of all of our present day, classical computers. We may think of a classical bit as a coin that is either heads or tails.
A quantum bit (qubit) is the quantum analog of a classical bit and can represent any combination of the numbers 0 and 1. And how are the qubits implemented in the present experiment? "The outermost electron of each ion," Britton explains, "acts as a tiny quantum magnet, known as spin
, and is utilized as a qubit. Quantum mechanics permits this spin to be in a superposition of states, for example simultaneously oriented parallel to, and antiparallel to, a laboratory magnetic field." Moreover, physically well-separated particles may be tightly interconnected, that is entangled. For example, two qubits can be in a state where both are always measured either in their 0 state or in their 1 state. If we were to add a third particle, its 0 and 1 states could each depend on any combination of the other two particles. This fact leads to an exponential growth in the number of variables: to represent N qubits, approximately 2N
numbers are required. This leads to insurmountable problems when trying to simulate quantum systems on today’s classical computers: the amount of memory and the number of computations required are simply too much to handle even for our most powerful supercomputers.
A different approach is therefore needed to study large interacting quantum systems. And this is where quantum simulators come in. By offering the ability to recreate interesting quantum effects in a controlled model setup, quantum simulators are expected to boost our understanding and advance engineering. Instead of air flow, quantum simulations often consider quantum bits, called spins. Here, we can think of a spin as a tiny magnet bar that can orient itself arbitrarily in three dimensions: "Previous experiments," Britton explains, "have used only about a dozen interacting spins. The NIST simulator, in contrast, permits controlled interaction of as many as 450 spins."
One field where quantum simulators can provide insight is the study of quantum phase transitions. Transitions between classical phases — gas, liquid, solid — are driven by thermal fluctuations. Quantum phase transitions, in contrast, are a consequence of quantum fluctuations that are present even at zero temperature. And, as we have seen above, this is the worst combination when it comes to computer simulations. For a quantum simulator, on the other hand, entanglement would simply be a feature of the setup, not a problem that needs to be addressed with tremendous amounts of RAM.
NIST’s quantum simulator would be suitable for simulating quantum magnetism, interacting spins arranged on the nodes of a flat grid — scientifically known as quantum Ising interactions on a two-dimensional lattice. "The Ising model," he continues, "describes a simple pair-wise interaction between pairs of spins on a lattice. Among its applications is explaining how weak short-range interactions can give rise to long-range ordering and bulk magnetization. Yet another application is the calculation of phase transitions in magnetic materials (e.g. from paramagnetic to ferromagnetic)."
"Britton’s simulator finally gets us closer to having a usable quantum simulator," says Tobias Schätz  from the Max Planck Institute of Quantum Optics in Garching, Germany. "Different groups have studied a variety of possibilities to building quantum simulators, and it now seems that trapped ions have allowed us to really get to the next level: that of developing quantum simulators that can simulate systems too complex for even our most powerful computers. Of course, we still have to study these new experiments very well to see how far we can trust their results, but I am very excited about Britton’s results." "Our technological world," Britton concludes, "depends greatly on ‘simple’ quantum devices like the Global Positioning System (GPS) and lasers. What’s needed is simulation support to guide the development of quantum materials such as, for example, high temperature superconductors."
 A. Niederberger, Visible and Entangled, Opt. Photon. Focus 3
, 7 (2008).
 A. Friedenauer, H. Schmitz, J. T. Glueckert, D. Porras & T. Schätz, Simulating a quantum magnet with trapped ions, Nat. Phys. 4
, 757-761 (2008).
2012 © Optics & Photonics Focus
AN is a Research Associate with the Department of Applied Physics at Stanford University, California, USA. His research focuses on quantum circuits, modeling of nano-photonic devices, and numerical optimization.
Joseph W. Britton, Brian C. Sawyer, Adam C. Keith, C.-C. Joseph Wang, James K. Freericks, Hermann Uys, Michael J. Biercuk & John J. Bollinger, Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins, Nature (2012) 484, 489-492 (link).