Abstract For the last chapter devoted to the interference of a particle, we go back a few years in time, to 1984. If until now everything has taken place in the familiar setting of old Europe (Fribourg, Vienna, Grenoble, Constance), this time the change of scene will be much greater – this year, the IEEE International Conference on Computers, Systems and Signal Processing, one of the most important gatherings of computer scientists and communication theoreticians, is taking place in the city of Bangalore, at the heart of the immense triangle that is India. However, all conference rooms look the same. Gilles Brassard, computer scientist from the University of Montreal, is not too dis- oriented when he is preparing himself to present a project done in collaboration with Charles Bennett, trained as a chemist, currently a theoretician at IBM in New York. The title of the lecture arouses the curiosity of those who glance absent-mindedly through the conference programme: Brassard is going to speak on ‘quantum cryptography’.
Abstract For the last chapter devoted to the interference of a particle, we go back a few years in time, to 1984. If until now everything has taken place in the familiar setting of old Europe (Fribourg, Vienna, Grenoble, Constance), this time the change of scene will be much greater – this year, the IEEE International Conference on Computers, Systems and Signal Processing, one of the most important gatherings of computer scientists and communication theoreticians, is taking place in the city of Bangalore, at the heart of the immense triangle that is India. However, all conference rooms look the same. Gilles Brassard, computer scientist from the University of Montreal, is not too dis- oriented when he is preparing himself to present a project done in collaboration with Charles Bennett, trained as a chemist, currently a theoretician at IBM in New York. The title of the lecture arouses the curiosity of those who glance absent-mindedly through the conference programme: Brassard is going to speak on ‘quantum cryptography’.
In our modern era of telecommunications and the Internet, information has become a valuable commodity. Sometimes it must therefore be protected against theft - in this case, loss of secret information to an eavesdropper. Most of today's transactions are protected using encryption unproven to be secure against a computational attack by a classical computer and, in fact, the standardly used encryption algorithms are provably vulnerable to the mind-boggling parallelism of a quantum computer, should one ever be physically realized. Enter quantum cryptography. Underlying nearly all forms of encryption is the necessity for a truly secret key, a random string of zeros and ones; the basic notion of quantum cryptography is to employ single photon transmissions (or the closest attainable approximation to these) to distribute the random key material, while removing the threat of an undetected eavesdropper. Now, nearly twenty years since the seminal quantum cryptography paper by Bennett and Brassard (Bennett C H and Brassard G 1984 Proc. IEEE Int. Conf. on Computers, Systems, and Signal Processing (Bangalore) (New York: IEEE) pp 175-9), we take a look at several state-of-the-art implementations, and glimpse how future quantum cryptosystems might look. We start with papers from three of the world's leading experimental quantum cryptography efforts: Stucki et al and Bethune and Risk describe working systems for quantum key distribution (QKD) over telecommunications fibres (at 1550 nanometres and 1300 nanometres, respectively). The former's achievement of quantum key exchange over 67 kilometres of optical fibre is a world record, as is the experimental demonstration by Hughes et al of daylight free-space QKD over a 10 km atmospheric range. Next, Lütkenhaus and Jahma explore the possible vulnerabilities of such systems (which employ attenuated laser pulses instead of actual single photon states) to conceivable future eavesdropping technologies. Enzer et al have implemented a totally new protocol, using polarization-entangled photons, which in some circumstances can tolerate higher error rates than the traditional one of Bennett and Brassard; moreover, the use of entanglement provides a means of `automatic source verification'. Finally, looking to the future, Elliott gives a provocative view of how these technologies may be merged into network operation, and Shapiro describes a method to combine a novel source of entangled photons with a means to transfer the photons' quantum state to trapped-atom quantum memories. If realized, these systems could presage the world's first quantum network. Focus on Quantum Cryptography Contents Quantum key distribution over 67 km with a plug&play system D Stucki, N Gisin, O Guinnard, G Ribordy and H Zbinden Autocompensating quantum cryptography Donald S Bethune and William P Risk Practical free-space quantum key distribution over 10 km in daylight and at night Richard J Hughes, Jane E Nordholt, Derek Derkacs and Charles G Peterson Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack Norbert Lütkenhaus and Mika Jahma Entangled-photon six-state quantum cryptography Daphna G Enzer, Phillip G Hadley, Richard J Hughes, Charles G Peterson and Paul G Kwiat Building the quantum network Chip Elliott Architectures for long-distance quantum teleportation Jeffrey H Shapiro Ground to satellite secure key exchange using quantum cryptography J G Rarity, P R Tapster, P M Gorman and P Knight Method for decoupling error correction from privacy amplification Hoi-Kwong Lo Paul G Kwiat University of Illinois at Urbana-Champaign, USA
As we have said, quantum mechanics has become the standard framework for most of what is done in physics and indeed has played this role for three-quarters of a century. For just as long, physicists and philosophers have, as we have already suggested, raised and discussed questions about the interpretation of quantum mechanics: Why do we single out measurement as a special kind of interaction that evokes a probabilistic, irreversible response from nature, when other kinds of interaction cause deterministic, reversible changes? How should we talk about quantum superpositions? What does entanglement tell us about the nature of reality? These are interesting questions and researchers still argue about the answers. However, in the last couple of decades researchers have also been thinking along the following line: Let us accept that quantum objects act in weird ways, and see if we can use this weirdness technologically. The two best examples of potential uses of quantum weirdness are quantum computation and quantum cryptography. One of the first quantum cryptographic schemes to appear in the literature, and the only one we consider in detail in this book, was introduced by Charles Bennett and Gilles Brassard in 1984. Their idea is not to use quantum signals directly to convey secret information. Rather, they suggest using quantum signals to generate a secret cryptographic key shared between two parties. Thus the Bennett–Brassard scheme is an example of “quantum key distribution.”
An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175--179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
Un ordinateur est un objet physique effectuant des opérations logiques, il a donc nécessairement besoin d’un substrat physique pour faire ces opérations. Aussi, si la théorie qui sous-tend l’informatique doit beaucoup aux mathématiciens (Turing pour n’en citer qu’un), c’est la physique qui a rendu la réalisation concrète des ordinateurs possible, qu’ils soient réalisés avec des relais électromécaniques, des tubes électroniques ou des transistors. Et cela ne s’arrête pas là : par exemple, d’une part la miniaturisation de ces derniers dans les processeurs fait que les phénomènes quantiques doivent être pris en compte (les électrons risquent de passer d’un fil à un autre par effet tunnel), d’autre part l’accroissement de la vitesse d’horloge rend concrète la barrière qu’est la vitesse de la lumière. Si les ordinateurs ne sont possibles qu’avec une théorie physique suffisamment évoluée, il y a une rétroaction qui se crée, car la physique a beaucoup bénéficié du développement des ordinateurs. Ceux-ci rendent en effet possibles des calculs – d’abord numériques, mais également symboliques – qu’il serait difficile de faire « à la main », pour des questions de temps et « d’erreurs humaines ». Cette possibilité a ouvert la voie à des simulations dans pratiquement toutes les branches de la physique, et ces simulations ont à leur tour pratique- ment créé de nouvelles branches, telle la théorie du chaos. En 1982, Richard Feynman déplorait cependant que les simulations informatiques de processus quantiques ne fussent pas efficaces, et suggérait qu’elles pourraient être bien plus rapides si l’ordinateur était lui-même « quantique » [2]. Dans ce document, nous allons d’abord revenir (chapitre 1) sur ce point et expliquer ce que pourrait faire différemment un ordinateur « quantique ». Nous décrirons ensuite (chapitre 2) les bases théoriques du calcul quantique tel que pourrait le pratiquer un ordinateur de ce type. Nous verrons finalement (chapitre 3) avec l’exemple de l’algorithme de Shor et de la Tranformation de Fourier Quantique qu’au-delà des simulations de processus quantiques, un ordinateur quantique pourrait accélérer dramatiquement d’autres opérations. Nous conclurons sur quelques approches possibles pour la réalisation d’un ordinateur quantique et sur l’existence d’autres applications de la mécanique quantique liées à l’informatique et à la communication qui ne nécessitent pas forcément un tel ordinateur, ainsi que sur des aspects plus philosophiques du calcul quantique.