Tomorrow we will have learned how to express the whole physics in the language of Information

John Archibald Wheeler

Frequently asked questions

What does it mean Quantum Information?

What is QUIT?

What is your aim?

What do you do?

What is Quantum Optics?

What is Quantum Teleportation?

What is Entanglement?

What is Quantum Tomography?

What is Quantum Cryptography?

 

What does it mean Quantum Information?

Quantum Information is currently one of the most rapidly developing areas of Physics, concerning both fundamental and applied issues related to Quantum Mechanics. It is becoming the basis of the future information technology, in the same way as the classical information theory of Shannon's in the fifties became the basics of the compression and cryptographic methods used for current telecommunications and computation. We have learned how to harness elusive quantum features, such as "complementarity" and "entanglement", in a way that now allows us to achieve secure communications on the basis of unbreakable physical laws---instead of mathematical algorithms---and in the future will allow us to perform computations in a way astonishingly faster than any conceivable computer based on the current technology. Quantum cryptography is already commercially viable: it has been demonstrated over distances of many kilometers. Quantum computers, on the other hand, are still at a preliminary stage: however, they are one of the main focus for current researches, since we know that the exponential progress that we have witnessed in computer technology will reach a saturation point in less than 10-15 years.

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Quantum mechanics, which up to ten years ago was considered only a major limitation to extreme nanotechnology, nowadays has become the basis of the new technology of "Quantum Information".

G.M.D.

What is QUIT?

QUIT means Quantum Information Theory Group. The group was founded at Pavia University by G. M. D'Ariano in the early 90's, and originally was the Quantum Optics Group. Since then the group has established numerous international collaborations with leading research groups in Quantum Optics and Quantum Information (Northwestern University, Oxford, Roma la Sapienza, Dussendorf, Braunschweig, Nottingham, Utrecht, Baltimore), has got many projects funded from UE, MIUR (Ministero dell'Istruzione, dell'Università e della Ricerca) and from INFM (Istituto Nazionale di Fisica della Materia). The group is member of the Network of Excellence of Quantum Information QUIPROQUONE and participates to scientific committees and organizing committees of national and international conferences.

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What is your aim?

Our aim is twofold. On one side, we want to establish the ultimate achievable performance limits of quantum evolutions in-principle, i.e. at the pure foundational level. On the other side, we want to actually design feasible implementations, for both new experiments of quantum mechanics and new applications for information technology. In our struggle for reaching the maximum allowable control in quantum coherence of quantum measurements we have already achieved and developed a new general method for the full characterization of quantum devices.

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The big fun with "Quantum Information" is that you can study the foundations of the enigmatic world of Quantum Mechanics, and, at the same time, you make something useful for practical applications.

G.M.D.

What do you do?

We are interested in everything concerns with quantum information theory and with quantum mechanics of measurements and open systems. One of the nice things about this fields is that you can address both foundational issues and applications to technology, also with the possibility of designing new experiments in quantum mechanics. For applications and for experiments we are mainly interested in quantum optics, since it is with the Laser light and non-linear optics that weirdness of quantum can be seen more easily. And, in fact, the only quantum teleportation experiments done up to now have been performed in laboratories of quantum optics.

As a theoretician of quantum information you have wide spectrum of different kinds of knowledges open for research, including quite cool mathematical physics, true foundational statistics, information theory, computer science, complexity theory, ... And you work with a very concrete style, addressing problems of security in cryptographic protocols, or of achieving the ultimate capacity of a quantum communication channel, or designing new devices that performs optimally desired quantum transformations or new kinds of measurements. An, as in any good engineering style, designing new devices requires to first prove feasibility, then to classify all possibilities, optimize them, and finally look for what is truly feasible in the lab, and in this way you move from the abstract mathematical level to the true experiment, and also to applications! This is an opportunity that seldom occurs in any other field in science.

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Although we had to do with Quantum Mechanics for an entire century, it is a yet too "mathematical", in the sense that it still lacks a purely physical foundation. Maybe the missing axiom is a physical principle of "informational" nature.

G.M.D.

What is Quantum Optics?

Quantum Optics was born with the advent of the laser (1960), which is able to produce extremely intense optical beams, by which one can exert nonlinear optical effects---e. g. frequency conversion---which would otherwise be negligible with conventional light. These effects on one side allow us to produce "entanglement"---the most elusive quantum feature and the main ingredient of the quantum information science---on the other hand they allow very strong and controlled interactions with atoms. In this way, Quantum Optics offers the unique opportunity of manipulating single atoms and photons, and controlling their interactions on a single quantum level with minimum "de-coherence". Quantum processors can be built by storing quantum information in internal states of trapped atoms or ions, and manipulating the atoms with lasers to implement quantum gates. Quantum effects are not only relevant for the new Quantum Information technology, but also for the "old" communication technology, e. g. in optical fibers, since the quantum uncertainty is the main source of noise (consider that an indetermination of just a single photon is equivalent to 10000 Kelvin of thermal noise). Thus Quantum Optics is the privileged field to study quantum mechanical effects, and the quantum optical labs have brought back Quantum Mechanics from the dusty shelfs of the academy to the hottest field of research. An this is why most of experiments in Quantum Information---e. g. quantum teleportation and quantum cryptography---have been done in quantum optical labs.

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What is Quantum Teleportation?

The "miracle" of quantum teleportation is also based on quantum nonlocality, i.e. "entanglement". "Teleportation" literally would mean to transfer at distance an object by just beaming the information about the state of its particles, not beaming the particles themselves (the particles are already available at the receiver, and they would be "indistinguishable" from those at the transmitter). However, Quantum Mechanics poses a fundamental problem to teleportation, since it dramatically limits the accuracy on the determining the state of any object, particle or wave, and one cannot experimentally determine an unknown state, (but at most one can distinguish between N mutually orthogonal states, provided one already knows which N states those are---for photons and spin-half particles, for example, N=2). Cloning (i. e. making perfect copies of) an unknown quantum state would allow to make a precise determination of the state by using many identical copies of it, but unfortunately, it is forbidden by Quantum Mechanics. On the other hand, we have also another problem: that, even if we know the state exactly (e. g. when we have prepared it) the information to transmit would be huge even for a single spin, since to specify its state we would need three real numbers (two for the angle and one for its length). Therefore, the precision in the transmission of even a single spin would be limited by the number of bits available. Therefore, in synthesis: a) we cannot know the quantum state; b) even if we knew it, we would need a virtually infinite information to transmit it. Now, how is it possible to "teleport" a quantum state? Here the astonishing result of Bennett, Brassard, Crépeau, Jozsa, Peres and Wootters: an unknown quantum state can be "teleported" from one place to another using only two bits per spin, along with a pair of entangled photons---this is the crucial ingredient! Alice and Bob (the transmitter and the receiver) each are each given one photon of the entangled pair. Then Alice brings together her particle and the particle in an unknown state, and performs jointly on those two particles a special measurement using a quantum gate. This measurement has four possible outcomes (here the two bits). Alice then communicates the result to Bob, by any ordinary channel (e. g. a telephone or radio). According to this result, Bob, who has the other particle of the entangled pair, performs one of four special operations on his particle, using another quantum gate. The overall effect is to leave Bob's particle in exactly the same state that Alice's particle was originally in. Et voila'!

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What is Entanglement?

Entanglement is certainly one of the most elusive features of Quantum Mechanics, and its study has turned into a very fruitful field of research, and it is only at its beginning. Entangled states were first investigated in the famous paper of Einstein, Podolsky and Rosen (EPR). Quantum Mechanics is "nonlocal", in the sense that distant and non-interacting systems may be "entangled", namely they can exhibit perfect and instantaneous correlations. For example, if Alice and Bob share a pair of entangled electron spins in a so-called "singlet" state (i. e. with total angular momentum zero), if Alice measures the spins vertically and finds it "up", then Bob for sure will find it "down" at the same time if he also measures it vertically. And, actually, they will always find the spins opposite, whichever direction they choose for the measurement. And you cannot think that maybe the two spins are two little demons that agreed in advance on a definite answer (i.e. up or down, right or left), since it has been proved as a mathematical theorem that in this way it is impossible to describe the correlations e. g. at 45 degrees! Therefore, either there are no hidden demons, or the demons must be "nonlocal", namely completely smeared between the two far-apart spins! It would be long to describe all applications of quantum entanglement, since it is the main ingredient of the whole Quantum Information science. It is also the basis of the "quantum parallelism" of Quantum Computers.

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What is Quantum Tomography?

Quantum Tomography is a kind of universal measurement scheme which allows to estimate the state of an object by performing many appropriate measurements on many copies of the same object prepared in the same state (the determination of the state from a single copy is forbidden by the "no-cloning" theorem). It is a powerful technique, which allows, for example, to determine experimentally how a quantum gate actually works, or to calibrate a new measuring apparatus. And, also here the quantum parallelism intrinsic of entanglement comes to help us, running all possible input states for the device in parallel by using only a single entangled state as the input. We just need to prepare two identical systems into an entangled state, and input only one of them into the device, leaving the other system untouched. Then we make the tomography of the joint state at the output.

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What is Quantum Cryptography?

A perfectly secure method to transmit information secretly is Vernam code or one-time pad. This means that the two parties share a secret sequence of random bits, and they sum each transmitted bit with one of the random sequence. The drawback of this method is that the secret sequence must be of the same length as the text to be encoded, and it can be used only once! So the problem of secrecy is just deferred from the message to the key, leading to the key distribution problem. Since often there is no practical way to distribute such large secret keys, most of today's cryptographic protocols rely on public key distribution, based on an assumed difficulty of computation problems. S. Wiesner, C. Bennett, and coworkers suggested how to use Quantum Mechanics to achieve provably secure key distribution, exploiting the disturbance that any measurement from a potential eavesdropper must produce, since, as Heisenberg teaches, no information can be gained without producing a disturbance. They showed how two communicating parties may agree on a random key by exchanging and manipulating quantum systems in such a way that the laws of nature guarantee that an eavesdropper will either reveal itself with near certainty or gain nearly no information about the key. The probability that an eavesdropper is not detected and nevertheless gains a substantial amount of information can be made as small as desired. Then, given secure key distribution, one then can use the secure Vernam cipher. This has the great advantage that it removes the risk (inherent in schemes that rely on the conjectured difficulty of some computational problem) of retroactive security loss due to unanticipated advances in hardware and algorithms, thus guaranteeing long-time security of the coded data. Quantum key distribution is the most advanced application of quantum information theory, and there have been many successful experiments in realistic circumstances. In these experiments the two-state quantum systems exchanged by the communicating parties are realized by qubits on the polarization of photons. In some experiments optical fibers are used to transmit the photons (currently, over distances of tens of kilometers: see, for example, at Los Alamos (USA), BT Labs (UK), the University of Geneva (CH), and the University of Vienna), in other photons are sent through the air (Los Alamos) with the ultimate goal of securing ground-to-satellite communications. Today's implementations of quantum cryptography still have some technical problems, mostly related to imperfections of the photon sources. Nevertheless, it is feasible, though at still rather low data rates (few hundreds of bits per second).

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