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arXiv:quant-ph/0107068 · Physical Review Letters

Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam

Xiaoying Li, Qing Pan, Jietai Jing, Jing Zhang, Changde Xie, Kunchi Peng

Published Jan 11, 2002• 450 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.88.047904

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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.
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.
A tripartite entangled state of bright optical field is experimentally produced using an Einstein-Podolsky-Rosen entangled state for continuous variables and linear optics. The controlled dense coding among a sender, a receiver, and a controller is demonstrated by exploiting the tripartite entanglement. The obtained three-mode "position" correlation and relative "momentum" correlation between the sender and the receiver, and thus the improvements of the measured signal to noise ratios of amplitude and phase signals with respect to the shot noise limit are 3.28 and 3.18 dB, respectively. If the mean photon number n equals 11 the channel capacity can be controllably inverted between 2.91 and 3.14. When n is larger than 1.0 and 10.52, the channel capacity of the controlled dense coding is predicted to exceed the ideal single channel capacity of coherent and squeezed state light communication, respectively.
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.
We have experimentally realized the scheme initially proposed as quantum dense coding with continuous variables [Ban, J. Opt. B: Quantum Semiclassical Opt. 1, L9 (1999); Braunstein and Kimble, Phys. Rev. A 61, 042302 (2000)]. In our experiment, a pair of EPR (Einstein-Podolsky-Rosen) beams is generated from two independent squeezed vacua. After adding a two-quadrature signal to one of the EPR beams, two squeezed beams that contain the signal were recovered. Although our squeezing level is not sufficient to demonstrate the channel capacity gain over the Holevo limit of a single-mode channel without entanglement, our channel is superior to conventional channels such as coherent and squeezing channels. In addition, the optical addition and subtraction processes demonstrated are elementary operations of universal quantum information processing on continuous variables.