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Journal of Experimental and Theoretical Physics Letters

Relativistic quantum cryptography for open space without clock synchronization on the receiver and transmitter sides

S. N. Molotkov

Published Nov 1, 2011• 7 citations
Publisher

Abstract

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 .

DOI
10.1134/s0021364011180093

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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 .
Relativistic quantum cryptography involves not only the geometric properties of the state vectors of a quantum system in the Hilbert space but also the properties of carriers of quantum states in the Minkowski spacetime. A physical type of quantum object carrying information with extremely high velocity in spacetime is of fundamental importance. The structure of spacetime, more precisely, irreducible representations of the Poincaré group, in the Hilbert space is responsible for the existence of massless particles, photons. In this sense, the structure of spacetime is in fact used in relativistic quantum cryptography systems for cryptographic key distribution. This makes it possible to guarantee the security of keys even with the use of orthogonal states .
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.
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.
The security of keys for the basic nonrelativistic BB84 protocol has been examined for more than 15 years. A simple proof of security for the case of a single-photon source of quantum states and finite sequences has been only recently obtained using entropy uncertainty relations. However, the existing sources of states are not strictly single-photon. Since sources are not single-photon and losses in a quantum channel—open space—are not a priori known and vary, nonrelativistic quantum cryptographic systems in open space cannot guarantee the unconditional security of keys. Recently proposed relativistic quantum cryptography removes fundamental constraints associated with non-single-photon sources and losses in open space. The resistance of a fundamentally new family of protocols for relativistic quantum key distribution through open space has been analyzed for the real situation with finite lengths of transmitted sequences of quantum states. This system is stable with real sources of non-single-photon states (weakened laser radiation) and arbitrary losses in open space.