More on Quantum Information

Quantum mechanics redefines information and its fundamental properties. Researchers at Perimeter Institute work to understand the properties of quantum information and study which information processing tasks are now feasible, and which are infeasible or impossible.  This includes research in quantum cryptography, which studies the trade-off between information extraction and disturbance, and its applications. It also includes research in quantum error correction, which involves the study of methods for protecting information against decoherence.

Quantum Information

Compared with our everyday experience, the quantum world – the world of the very small, of atoms and elementary particles – is incredibly bizarre. For example, it is possible for a single particle to behave as if it were in more than one place at the same time. Also, our notion of what is separate and what is not breaks down in the quantum world: particles could be kilometres apart and still, in some respects, act like a single entity.

As strange as it may be, there is little question that this is how the quantum world works, as hundreds of experiments and many highly successful technological applications have shown: for example, the transistor (the basis of most of our current computing technology), the laser (the basis of today’s fiber optic communication networks and many other technologies), MRI (Magnetic Resonance Imaging) devices crucial to modern medicine, SQUIDs (Superconducting Quantum Interference Devices) used to search for new oil deposits or scan magnetic activity in the brain, and many more.

Currently, physicists are working on yet another quantum application. Their goal is to harness quantum weirdness to develop new technologies that will take us from the information age into the quantum information age. This has already resulted in quantum cryptography, the most secure form imaginable of sending secret messages. The hope is that it will also lead to the practical realization of a new type of computer, a quantum computer, able to solve certain types of problems much faster than any standard computer could.

Quantum Cryptography

Our modern world relies heavily upon the techniques of cryptography – the science and technology of creating, transmitting, and deciphering secret messages.

In ordinary cryptography, the sender of a secret message (Alice) uses a key to encrypt, or scramble the message, and the receiver (Bob) uses the same key to decrypt, or unscramble the message. Absolute security relies on only Alice and Bob knowing the key, and on using the key only once. With quantum cryptography, it is possible to distribute random number keys to Alice and Bob in such a way that any attempt to eavesdrop on this quantum key distribution (QKD) process is guaranteed to be detected. The guaranty is a result of the quirky quantum nature of our universe, and is completely impervious to how clever the eavesdropper may be, or how advanced their technology. 

              

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Artist's conception of quantum key distribution over free space ground to satellite quantum information links.© ESA              

 

 

Techniques for QKD rely on one or both of two important properties of our quantum world. The first is that quantum systems like photons (particles of light) are very delicate, and thus easily disturbed by any measurement performed on them, and eavesdropping necessarily involves measurement. The second is that it is possible to entangle (see quantum foundations) a pair of quantum systems, like two photons, such that even if they are separated by kilometres, they behave in some respects as a single system:  performing a measurement on one of the pair of photons will affect the other. Such entangled pairs of photons can be sent to Alice and Bob, and by following a certain recipe for measuring their photons, they can generate a secret shared random number key, which they can then use to send their message, even over a public communication channel, with absolute security. 

There are currently several commercial implementations of such quantum cryptography systems, operating over distances of several kilometres. One of many exciting areas of research is the development of free space QKD links capable of operating between ground stations and satellites, which might lead to a global, absolutely secure quantum communication network.

Quantum Computers

All information processed by a computer (such as the one you are using now) is processed in terms of bits – elementary units of information that can be in one of two possible states. These states are usually referred to as 0 and 1. All the information on your computer is stored in coded form as long sequences of zeroes and ones. For instance, a sequence of three bits allows for eight different combinations, and can thus represent eight different numbers (or letters, or cities, etc): 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, and 111=7. 

In a quantum computer, the situation is fundamentally richer. To see why, we must first recognize that any computing machine stores information not abstractly, but rather in some concrete physical form: for example, the location of beads on an abacus, the electric current through a transistor in an ordinary computer, or electrical impulses traveling along neurons in your brain. In a conventional computer, the 0 state might be represented by the transistor being "off" (no current), and 1 by "on" (current flowing). Information is thus physical, and as such, the processing of information is subject to the laws of physics.

              

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Binary information (0 or 1) can be stored in the physical state of an electron (spin down or spin up)             

 

 

Ordinary computers do rely on the laws of quantum physics. Transistors are quantum devices, but transistors are traditionally too large to be able to harness the full potential of quantum weirdness, which happens at the scale of atoms and subatomic particles. However, technology has now advanced to such a degree that we are able to construct and manipulate devices at the atomic scale. This means we have the potential to create computers that store and process information in a fully quantum way.

For example, an electron is a remarkable, purely quantum "device" that behaves somewhat like a tiny, perpetually spinning bar magnet. If it is placed in the field of another magnetic, it has two natural states, either aligned with the field, or opposite to it. We call these two states spin up and spin down. Thus the electron can be used to store one bit of information, say spin down = 0, spin up = 1.

So far, this is the same as an ordinary computer, except that the information is stored in an incredibly small space. For example, the information may be stored in electrons, and so each bit of information occupies the space of an atom, which is much smaller than in any conventional storage medium such as your computer's hard disk.

Now we come to the quantum "magic." We noted above that one bizarre feature of the quantum world is that it is possible for a single particle to behave as if it is in more than one place at the same time. This is a general property of the quantum world – things can exist simultaneously in more than one state, called the principle of superposition (see quantum foundations). In the case of the electron, it can exist in both spin up and spin down states simultaneously. In other words, instead of just 0 or 1, it can be 0 and 1.

How does this help us? If we have, say, three such "quantum bits," or "qubits," then instead of just being in the states 000 or 001 or 010, etc. (the eight possibilities listed above), they can be, in a certain sense, in all these states simultaneously. It is then possible to manipulate these qubits, using the laws of quantum physics, to perform multiple calculations simultaneously: a quantum-parallel computer. This quantum parallelism results in computing power that grows exponentially, doubling with each additional qubit. Adding 1 qubit increases the computing power by a factor of 2. Adding 2 qubits increases it by 4. Adding 3 qubits increases it by 8, and so on. With just a hundred qubits, the raw computing power would far exceed anything we might hope to achieve with a conventional computer.

              

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Three qubits can be in a quantum superposition of multiple states simultaneously, in this case 011, 100 and 101.

However, the trick is in how these qubits are "manipulated," which is the quantum analogue of a conventional computer program telling the computer what kind of calculation to perform. So far there are only a few kinds of problems that we know how to ask a quantum computer to solve, although, to be sure, these problems are of great practical importance. One of them, the question of how to write a given, very large number as a product of prime numbers, is at the heart of one of the most commonly used methods of modern encryption. With a working quantum computer, you could easily decipher encrypted messages currently floating around on the Internet between banks, governments, and so forth. (However, even a quantum computer cannot be used to eavesdrop on the quantum key distribution process discussed above!) Theoretical physicists and mathematicians are currently working very hard to expand the types of problems a quantum computer could be asked to solve.

There are also a number of experimental challenges. Most importantly, as we saw in our discussion of quantum cryptography, quantum information – stored in superposition and entangled states – is very delicate, and easily destroyed by outside influences. Ideally, a quantum computer must be perfectly isolated from its environment while it is performing its quantum-parallel computation. Of course in practice this is not possible, resulting in random errors in computation. Nevertheless, physicists and computer scientists have built upon the classical theory of fault-tolerant error correction (necessary to stabilize conventional computations running in unstable environments or running for very long periods of time), to develop a set of techniques that allow us to protect quantum information from realistic errors. These techniques require good, but not perfect, control of a quantum system, and experimental physicists and engineers worldwide are working toward developing quantum computers that will be robust in the real world.

              

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The ability to distribute pairs of entagled particles [more]. © Vienna University, photo by Robin Riegler. 

So far, quantum computers are mostly a theoretical construct, although very simple proof-of-principle versions have been built. Once experimental physicists succeed in constructing large quantum computers, we should be able to harness the weirdness of the quantum world to perform, in seconds, certain types of calculations which, on a conventional computer, would take thousands of years.

              

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In the presence of a strong magnetic field, some atomic nuclei can be in one of two states [more]         

Figure courtesy IQC.

Such attempts to harness the quantum world to create powerful and practical new technologies forces physicists to think more deeply about how the universe works – the foundations of quantum theory, which in turn may lead to new insights into the biggest problem of all: combining the quantum and relativity theories into a single, unified theory of quantum gravity.

              

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Quantum teleportation allows physicists to transport quantum information from one part of a quantum computer to another [more]

To learn more about quantum information at Perimeter Institute and the researchers, please click here.

 

Perimeter Institute Resources

Public Lectures
The following selection of Perimeter Institute multi-media presentations by leading scientists is particularly relevant to quantum information. Click on the link to read a full description of each talk and choose your viewing format.

Specially for Teachers and Students
These multi-media talks by Perimeter Institute researchers and visiting scientists were presented to youth and educators during Perimeter Institute’s ISSYP, EinsteinPlus or other occasions.

Suggested External Resources

  • Quantum computing – article on the IQC website (basic).
  • Brown, Julian.  Minds, Machines, and the Multiverse:  The Quest for the Quantum Computer.  Simon & Schuster, 2000.
  • Deutsch, David.  The Fabric of Reality: The Science of Parallel Universes and Its Implications.  Penguin Books, 1997.  (basic)
  • Milburn, Gerard.  Schrodinger’s Machines:  The Quantum Technology Reshaping Everyday Life.  W H Freeman & Co, 1997.  (basic).
  • Mosca, M., Jozsa, R., Steane, A., and Ekert, A.  Quantum-Enhanced Information Processing.  Visions of the Future:  Physics and Electronics.  Editor J.M. Thompson.  Cambridge University Press, 2001.
  • Nielson, Michael.  Rules for a Complex Quantum World.  Scientific American, November 2002.

Compared with our everyday experience, the quantum world – the world of the very small, of atoms and elementary particles – is incredibly bizarre.