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arXiv:quant-ph/9909030 · Physical Review A

Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations

M. D. Reid

Published Nov 1, 2000• 193 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.62.062308

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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.
Quantum cryptography with the predetermined key was experimentally realized using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical beams. Only one of two EPR correlated beams is transmitted with the signals modulated on quadrature phases and amplitudes, and the other one is retained by the authorized receiver. The modulated small signals are totally submerged in the large quantum noise of the signal beam, therefore nobody except the authorized receiver can decode the signals. Usability of imperfect quantum correlation, high transmission and detection efficiencies, and security provided by quantum mechanics are the favorable features of the presented scheme.
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.
Highly efficient quantum dense coding for continuous variables has been experimentally accomplished by means of exploiting a bright Einstein-Podolsky-Rosen (EPR) beam with anticorrelation of amplitude quadratures and correlation of phase quadratures. Two bits of classical information are encoded on two quadratures of a half of a bright EPR beam, then are simultaneously decoded by the other half of the EPR beam with the sensitivities beyond that of the shot noise limit. A high degree of immunity to unauthorized eavesdropping has been experimentally demonstrated.