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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Relativistic quantum cryptography

S. N. Molotkov, S. S. Nazin

Published Jul 23, 2003• 0 citations
Publisher

Abstract

The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistitic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not empoly collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of "antedate" coding).

DOI
10.1117/12.517871

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The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistitic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not empoly collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of "antedate" coding).
One of the central points of quantum information theory is the problem of ultimate security of quantum cryptography; i.e., the security that is due only to the fundamental laws of nature rather than to technical restrictions. It is shown that a relativistic quantum cryptosystem proposed in this paper is ultimately secure against any eavesdropping attempts. The application of relativistic causality makes it possible to simply prove the security of the cryptosystem. Moreover, because the scheme does not involve collective measurements and quantum codes, it can be experimentally implemented even at the current level of optical fiber technologies.
Whereas quantum cryptography ensures security by virtue of complete indistinguishability of nonorthogonal quantum states attenuation in quantum communication channels and unavailability of single-photon sources present major problems. In view of these difficulties the security of quantum cryptography can change from unconditional to conditional. Since the restrictions imposed by nonrelativistic quantum mechanics and used to formulate key distribution protocols are largely exhausted new principles are required. The fundamental relativistic causality principle in quantum cryptography can be used to propose a new approach to ensuring unconditional security of quantum cryptosystems that eliminates the aforementioned difficulties. Quantum cryptosystems of this kind should obviously be called relativistic. It is shown that relativistic quantum cryptosystems remain unconditionally secure: first attenuation in a quantum communication channel can only reduce the key generation rate but not the security of the key second the source may not generate pure single-photon states and a nonzero single-photon probability will suffice. The scheme remains secure even if the contribution of a single-photon component is arbitrarily small. This formally implies that a state may be characterized by an arbitrarily large mean photon number. The single-photon probability affects only the key generation rate but not security.
A simple proof of the unconditional security of a relativistic quantum cryptosystem based on orthogonal states is given. Limitations imposed by the special relativity theory allow the proof to be markedly simplified as compared to the case of nonrelativistic cryptosystems based on nonorthogonal states. An important point in the proposed protocol is a space-time structure of the quantum states, which is ignored in the non-relativistic protocols using only the properties of the space of states of the information carriers. As a consequence, the simplification is related to the inefficacy of using the collective measurements against an eavesdropper, the allowance for which is an especially difficult task in the nonrelativistic case.
Whereas quantum cryptography ensures security by virtue of complete indistinguishability of nonorthogonal quantum states, attenuation in quantum communication channels and the unavailability of single-photon sources present major problems. In view of these difficulties, the security of quantum cryptography can change from unconditional to conditional. Since the restrictions imposed by nonrelativistic quantum mechanics and used to formulate key distribution protocols have been largely exhausted, new principles are required. The fundamental relativistic causality principle in quantum cryptography can be used to propose a new approach to ensuring unconditional security of quantum cryptosystems that eliminates the aforementioned difficulties. Quantum cryptosystems of this kind should obviously be called relativistic. It is shown that relativistic quantum cryptosystems remain unconditionally secure: first, attenuation in a quantum communication channel can only reduce the key generation rate, but not the security of the key; second, the source may not generate pure single-photon states, and a nonzero single-photon probability will suffice. The scheme remains secure even if the contribution of a single-photon component is arbitrarily small. This formally implies that a state may be characterized by an arbitrarily large mean photon number. The single-photon probability affects only the key generation rate, but not security.
Quantum cryptography aims at solving the everlasting problem of unconditional security in private communication. Every time we send personal information over a telecom channel a sophisticate algorithm protect our privacy making our data unintelligible to unauthorized receivers. These protocols resulted from the long history of cryptography. The security of modern cryptographic systems is guaranteed by complexity: the computational power that would be needed for gaining info on the code key largely exceed available one. Security of actual crypto systems is not “by principle” but “practical”. On the contrary, quantum technology promises to make possible to realize provably secure protocols. Quantum cryptology exploits paradigmatic aspects of quantum mechanics, like superposition principle and uncertainty relations. In this contribution, after a brief historical introduction, we aim at giving a survey on the physical principles underlying the quantum approach to cryptography. Then, we analyze a possible continuous variable protocol.
The security of keys in quantum cryptography is based on fundamental quantum mechanical exclusions (the exclusion of cloning and copying of nonorthogonal quantum states. The physical type of a quantum object that carries information (photon, electron, atom, etc.) is insignificant; only its state vector is important. In relativistic quantum cryptography for open space, both the time of the information carrier (photon that propagates with the extremely allowable velocity in a vacuum) and its quantum state are of fundamental importance. Joint fundamental constraints that are dictated by both special relativity and quantum mechanics on the discrimination of nonorthogonal quantum states allow one to formulate fundamentally new key distribution protocols that are stable against any attacks on a key and guarantee the security of keys for a nonstrictly single-photon source and any losses in the communication channel. Although this protocol is a real-time protocol in the Minkowski space-time, where the attack to the communication channel is detected by the delay of eavesdropper measurement results, the protocol does not require clock synchronization on the transmitter and receiver sides .