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arXiv:quant-ph/0112039

The Einstein-Podolsky-Rosen Paradox and Entanglement 2: Application to Proof of Security for Continuous Variable Quantum Cryptography

M. D. Reid

Published Dec 7, 2001• 0 citations

Abstract

In a previous paper certain measurable criteria have been derived, that are sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR) correlations for measurements with continuous variable outcomes. Here it is shown how such EPR criteria, which do not demand perfect EPR correlations, can be used to prove the extent of security for continuous variable quantum cryptographic schemes (in analogy to that proposed by Ekert) where Alice and Bob hope to construct a secure sequence of values from measurements performed on continuous-variable EPR-correlated fields sent from a distant source. It is proven that the demonstration of the EPR criterion on Alice's and Bob's joint statistics compels a necessary loss in the ability to infer the results shared by Alice and Bob, by measurements performed on any third channel potentially representing an eavesdropper (Eve). This result makes no assumption about the nature of the quantum source of the fields transmitted to Alice and Bob, except that the EPR correlations are observed at the final detector locations. In this way a means is provided to establish security in the presence of some loss and less than optimal correlation, and against any eavesdropping strategy employed by Eve prior to detection of the fields by Alice and Bob.

DOI: 10.48550/arxiv.quant-ph/0112039

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Correlations of the type discussed by EPR in their original 1935 paradox for continuous variables exist for the quadrature phase amplitudes of two spatially separated fields. These correlations were first experimentally reported in 1992. We propose to use such EPR beams in quantum cryptography, to transmit with high efficiency messages in such a way that the receiver and sender may later determine whether eavesdropping has occurred. The merit of the new proposal is in the possibility of transmitting a reasonably secure yet predetermined key. This would allow relay of a cryptographic key over long distances in the presence of lossy channels.

In this paper security of the quantum key distribution scheme using correlations of continuous variable Einstein–Podolsky–Rosen (EPR) pairs is investigated. A new approach for calculating the secret information rate Δ I is proposed by using the Shannon information theory. Employing an available parameter F which is associated with the entanglement of the EPR pairs, one can detect easily the eavesdropping. Results show that the proposed scheme is secure against individual beam splitter attack strategy with a proper squeeze parameter.

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