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Journal of Modern Optics

Three-state quantum cryptography

Simon J. D. Phoenix, Stephen Mark Barnett, Anthony Chefles

Published Feb 1, 2000• 74 citations
Publisher

Abstract

We introduce a protocol for quantum key distribution using three mutually non-orthogonal states. The protocol generates key bits most efficiently for three symmetric states. The generalized measurements which minimize the error probability and maximize the mutual information for such a system are known and can be implemented optically. We analyse eavesdropping strategies based on these optimal measurements.

DOI
10.1080/09500340008244056

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We introduce a protocol for quantum key distribution using three mutually non-orthogonal states. The protocol generates key bits most efficiently for three symmetric states. The generalized measurements which minimize the error probability and maximize the mutual information for such a system are known and can be implemented optically. We analyse eavesdropping strategies based on these optimal measurements.
We have implemented the 'six-state' quantum cryptography protocol using polarization-entangled photon pairs, in which the polarization of each photon of a pair is measured in one of three randomly chosen bases. For a given amount of eavesdropping, this protocol results in a larger error rate than in four- or two-state protocols, but reduces the number of key-producing events. We have experimentally investigated several incoherent eavesdropping strategies, and verified the predicted enhancement in error rate. However, we demonstrate that for low error rates, the efficiency for secret key generation is higher when using the four-state protocol.
Quantum key distribution(QKD) is one of the most significant areas in quantum information theory. For nearly four decades, substantial QKD protocols and cryptographic methods are developed. In early years, the security of protocols are depend on switching different bases, which, in fact, are based on non-orthogonal states. The most famous example is the BB84 protocol. Later, other techniques were developed for orthogonal states cryptography. Representations of such protocols including the GV protocol and order-rearrangement protocols. It might be harder to implement protocols based on orthogonal states since they require extra techniques to obtain security. In this paper, we give two QKD protocols based on orthogonal states. One of them needs not to employ order-rearrangement techniques while the other needs. We give analyses of their security and efficiency. Also, anti-noisy discussions would be given. Our protocols are highly efficient when considering consumptions of both qubits and classical bits while they are robust over several noisy channels. Moveover, the requirements of maximally entangled states maybe less than previous protocols and so the efficiency of measurements may be increased.
A generalization of the quantum cryptographic protocol by Bennett and Brassard is discussed, using three conjugate bases, i.e., six states. By calculating the optimal mutual information between sender and eavesdropper it is shown that this scheme is safer against eavesdropping on single qubits than the one based on two conjugate bases. We also address the question for a connection between the maximal classical correlation in a generalized Bell inequality and the intersection of mutual informations between sender/receiver and sender/eavesdropper.
When eavesdropping on a quantum channel, two distinct properties of quantum physics arise. First, if the quantum system is prepared in one of several non-orthogonal states, then no measurement can discriminate these states with certainty. Second, any measurement that acquires information about a system must necessarily disturb it. We investigate a simple and optimal eavesdropping scheme that minimizes the disturbance caused by a given amount of information gain, and show that an in principle demonstration of such a scheme could be performed using existing experimental techniques in single-photon quantum technologies.