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Journal of Experimental and Theoretical Physics Letters

Experimental scheme of quantum cryptography on the nonorthogonal states with time shift and a minimum number of optical components

S. N. Molotkov

Published Nov 1, 2003• 1 citation
Publisher

Abstract

A new scheme of experimental quantum cryptography on the nonorthogonal states is described. Nonorthogonality is achieved by the time shift of states in different messages. For this scheme to be efficient, it is sufficient to balance the arms of an interferometer at the receiver and transmitter ends to an accuracy of 1–2 cm. This is a fundamental advantage of this scheme over, e.g., the most developed cryptosystem based on phase coding, where the maximum transmission distance has been achieved. In the latter system, the arms of the interferometer need to be balanced with an accuracy of fractions of a micron for a distance of several tens of kilometers.

DOI
10.1134/1.1644313

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A new scheme of experimental quantum cryptography on the nonorthogonal states is described. Nonorthogonality is achieved by the time shift of states in different messages. For this scheme to be efficient, it is sufficient to balance the arms of an interferometer at the receiver and transmitter ends to an accuracy of 1–2 cm. This is a fundamental advantage of this scheme over, e.g., the most developed cryptosystem based on phase coding, where the maximum transmission distance has been achieved. In the latter system, the arms of the interferometer need to be balanced with an accuracy of fractions of a micron for a distance of several tens of kilometers.
The prototype of a new quantum cryptosystem is described. Such a cryptosystem is naturally called time-shift quantum cryptography. It realizes all basic quantum-cryptography protocols [BB84, B92, BB84(4+2)] in a common fiber-optic system. This scheme does not involve Mach-Zehnder interferometers, which enables one to naturally realize the multiplex mode of secure key distribution and to naturally integrate this quantum-cryptography scheme into traditional fiber-optic telecommunication systems. The proposed time coding method in quantum cryptography makes it possible to significantly simplify experimental schemes and to exclude the finest fiber-optic part, the interferometer. In essence, the fundamental difference of the time coding method from the phase coding method is that the part using phase relations in superposition between “parts” of a quantum state is eliminated from the phase-coding method, and only the part using the time division principle is retained. The time division principle is common for both methods and is minimally necessary, in contrast to the phasecoding method, which can be excluded altogether. The proposed scheme is briefly compared with the two most developed phase-coding schemes (without self-compensation and with passive self-compensation).
Three fundamentally new experimental prototypes of optical fiber quantum-cryptography schemes are described. They are appreciably simpler than the available prototypes, contain fewer optical fiber components, and do not require adjustment during key generation. These cryptosystems can naturally be called quantum time-shift cryptography. They realize the B92 protocol and use a pair of nonorthogonal single-photon states as information states. One such scheme does not use fiber-optic Mach-Zehnder interferometers and, therefore, provides natural realization of the multiplex secure-key distribution regime.
All existing quantum cryptosystems use nonorthogonal states as the carriers of information. Nonorthogonal states cannot be cloned (duplicated) by an eavesdropper. As a result, any eavesdropping attempt must introduce errors in the transmission, and, therefore, can be detected by the legal users of the communication channel. Orthogonal states are not used in quantum cryptography, since they can be faithfully cloned without altering the transmitted data. We present a cryptographic scheme based on orthogonal states, which also assures the detection of any eavesdropper.
In so-called private-key cryptographic systems, secure transmission of confi dential information through unprotected channels relies on the exchange of secret keys, known only to the sender, Alice, and the receiver, Bob.Quantum cryptography is based on the properties of quantum mechanics to obtain a provably secure key distribution.Most existing implement ations rely on either the polarization or the phase of very weak pulses of light sent through optical fibers.Recent results by research groups in British Telecom, Los Alamos National Laboratory and at the University of Geneva, have shown that quantum key distribution is possible over distances of tens of kilometers, using only standard telecom cables.However, due to birefringence and the effects of the environment, the polarization at the output of a fiber fluctuates randomly.Therefore, all existing systems need active polarization control.Systems based on phase also require interferometric detection, which necessitates active stabilization of the interferometers.To eliminate these problems, our team, led by Prof. N. Gisin in the Group of Applied Physics at the University of Geneva, is currently developing a new interferometric system implementing phase-encoded quantum key distribution (US patent pending).A schematic of the setup is given in Fig. 1.Its main features are:1) The system is based on time multiplexing, the interfering pulses following exactly the same spatial path, albeit with a small time delay.The interferometer is thus automatically aligned, and needs neither adjustments nor stabilization of the path lengths.2) Use of Faraday mirrors enables all birefringence effects in the fibers to be cancelled out.Therefore, the system does not require any polarization control.With this new system, Alice and Bob could exchange their cryptographic keys through standard telecom systems.They would be provided with a sending kit and
Although it is known that any two nonorthogonal pure states can constitute a secure quantum cryptosystem, the generalization of this scheme to the use of two mixed states is not trivial. It is shown here that even if a condition corresponding to the nonorthogonality in the pure-state case is satisfied, the mixed-state cryptosystem is still vulnerable to attack by an eavesdropper. A necessary and sufficient condition for the secure communication is derived. It states that the two mixed states must be connected by a rotation operator with a nonorthogonal angle.
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 .