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arXiv:quant-ph/0612087 · Physical Review A

Dense-coding quantum key distribution based on continuous-variable entanglement

Xiaolong Su, Jietai Jing, Qing Pan, Changde Xie

Published Dec 11, 2006• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.74.062305

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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.
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 this paper, we present the first experimental demonstration on continuous variable quantum key distribution using determinant Einstein-Podolsky-Rosen entangled states of optical field. By means of the instantaneous measurements of the quantum fluctuations of optical modes, respectively, distributed at sender and receiver, the random bits of secret key are obtained without the need for signal modulation. The post-selection boundaries for the presented entanglement-based scheme against both Gaussian collective and individual attacks are theoretically concluded. The final secret key rates of 84 kbits/s and 3 kbits/s are completed under the collective attack for the transmission efficiency of 80% and 40%, respectively.
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.
A quantum key distribution protocol, based on the quantum dense encoding in entangled states, is presented. In this protocol, we introduce an encoding process to encode,two classical bits information into one of the four one-qubit unitary operations implemented by Alice and the Bell states measurement implemented by Bob in stead of direct measuring the previously shared Einstein-Podolsky-Rosen pairs by both of the distant parties, Alice and Bob Considering the practical application we can get the conclusion that our protocol has some advantages. It not only simplifies the measurement which may induce potential errors, but also improves the effectively transmitted rate of the generated qubits by the raw key. Here we also discuss eavesdropping attacks against the scheme and the channel loss.
In a practical quantum communication system, the security of signal source of continuous-variable quantum key distribution may be jeopardized due to device flaws and hidden attacks. In this paper, an improved scheme for Gaussian-modulated continuous-variable quantum key distribution based on an untrusted entangled source is proposed. In particular, the entanglement source is placed in an untrusted quantum channel to simulate that it is controlled by an eavesdropper, thereby verifying the security of Gaussian-modulated continuous-variable quantum key distribution in a complex environment. This work in detail analyzes the influence of untrusted entanglement source on practical Gaussian-modulated continuous-variable quantum key distribution system, and the numerical simulation shows that the performance of Gaussian-modulated continuous-variable quantum key distribution will dramatically decrease once the entanglement source has moved out of the sender, and it will slightly rise as the untrusted entanglement source slowly moves away from the sender. This paper further introduces two kinds of optical amplifiers, which are phase-sensitive amplifier and phase-insensitive amplifier, to compensate for the imperfection of the coherent detector. These amplifiers are beneficial to enhancing the quantum efficiency of the receiver’s detector. Specifically, the security key rate of Gaussian-modulated continuous-variable quantum key distribution with homodyne detection can be well improved by phase-sensitive amplifier, and the security key rate of Gaussian-modulated continuous-variable quantum key distribution with heterodyne detection can be well improved by phase-insensitive amplifier. To summary, this paper proposes a scheme for Gaussian-modulated continuous-variable quantum key distribution with untrusted entanglement source, experimental results show that the proposed scheme can generate secure quantum keys even if the Gaussian entanglement source is untrusted, and the two optical amplifiers can effectively improve the quantum efficiency of the detector at the receiver. This work aims to promote the practical process of the Gaussian-modulated continuous-variable quantum key distribution system and provide theoretical guidance for the practical implementation and application of the Gaussian-modulated continuous-variable quantum key distribution system.
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.