Quantum cryptography

Abstract: Practical application of the generalized Bells theorem in the so-called key distribution process in cryptography is reported. The proposed scheme is based on the Bohms version of the Einstein-Podolsky-Rosen gedanken experiment and Bells theorem is used to test for eavesdropping. © 1991 The American Physical Society.

Abstract: Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Abstract: All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory} But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding However, it appeared that this new resource is very complex and difficult to detect Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon A basic role of entanglement witnesses in detection of entanglement is emphasized

Abstract: When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of disturbing the transmission in such a way as to be detected. Such a quantum channel can be used in conjunction with ordinary insecure classical channels to distribute random key information between two users with the assurance that it remains unknown to anyone else, even when the users share no secret information initially. We also present a protocol for coin-tossing by exchange of quantum messages, which is secure against traditional kinds of cheating, even by an opponent with unlimited computing power, but ironically can be subverted by use of a still subtler quantum phenomenon, the Einstein-Podolsky-Rosen paradox.