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arXiv:quant-ph/0204111

Quantum Cryptography Using Einstein-Podolsky-Rosen Correlations of Continuous Variables

Jietai Jing, Qing Pan, Changde Xie, Kunchi Peng

Published Apr 19, 2002• 4 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0204111

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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.
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.
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.
We proposed a scheme of continuous-variable quantum key distribution, in which the bright Einstein-Podolsky-Rosen entangled optical beams are utilized. The source of the entangled beams is placed inside the receiving station, where half of the entangled beams are transmitted with round trip and the other half are retained by the receiver. The amplitude and phase signals modulated on the signal beam by the sender are simultaneously extracted by the authorized receiver with the scheme of the dense-coding correlation measurement for continuous quantum variables, thus the channel capacity is significantly improved. Two kinds of possible eavesdropping are discussed. The mutual information and the secret key rates are calculated and compared with those of unidirectional transmission schemes.
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.