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arXiv:quant-ph/0101043 · Physical Review A

Efficient quantum-key-distribution scheme with nonmaximally entangled states

Peng Xue, Chuan‐Feng Li, Guang‐Can Guo

Published Aug 14, 2001• 54 citations
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Abstract

We propose an efficient quantum-key-distribution scheme based on entanglement. The sender chooses pairs of photons in one of the two equivalent nonmaximally entangled states randomly, and sends a sequence of photons from each pair to the receiver. The sender and receiver choose from the various bases independently but with substantially different probabilities, thus reducing the fraction of discarded data, and a significant gain in efficiency is achieved. We then show that refined data analysis like that proposed by Lo et al. (H. K. Lo, H. F. Chau, and M. Adrehali, e-print quant-ph/0011056) guarantees the security of our scheme against a biased eavesdropping strategy. Remarkably, our scheme is more efficient than distillation of singlets out of the nonmaximally entangled states and biased detection afterward.

DOI
10.1103/physreva.64.032305

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We propose an efficient quantum-key-distribution scheme based on entanglement. The sender chooses pairs of photons in one of the two equivalent nonmaximally entangled states randomly, and sends a sequence of photons from each pair to the receiver. The sender and receiver choose from the various bases independently but with substantially different probabilities, thus reducing the fraction of discarded data, and a significant gain in efficiency is achieved. We then show that refined data analysis like that proposed by Lo et al. (H. K. Lo, H. F. Chau, and M. Adrehali, e-print quant-ph/0011056) guarantees the security of our scheme against a biased eavesdropping strategy. Remarkably, our scheme is more efficient than distillation of singlets out of the nonmaximally entangled states and biased detection afterward.
The authors call attention to previous work with related result, a quantum-key-distribution scheme based on partial unknown entanglement with Wigner's inequality to establish the security of the quantum channel. The sender chooses any entangled state from a certain set or its equivalent state randomly, and sends a sequence of particles out of each pair to the receiver. The two users each choose between two measurements along the fixed axes. In fact, this is a quantum cryptosystem based on mixed entanglement. The main paper was published in Phys. Rev. A 64, 032305 (2001).
We investigate a quantum key distribution (QKD) scheme that utilizes a biased basis choice in order to increase the efficiency of the scheme. The optimal bias between the two measurement bases, a more refined error analysis and finite key size effects are all studied in order to assure the security of the final key generated with the system. We then implement the scheme in a local entangled QKD system that uses polarization entangled photon pairs to securely distribute the key. A 50/50 non-polarizing beamsplitter (BS) with different optical attenuators is used to simulate a variable BS in order to allow us to study the operation of the system for different biases. Over 6 h of continuous operation with a total bias of 0.9837/0.0163 ( Z / X ), we were able to generate 0.4567 secure key bits per raw key bit as compared to 0.2550 secure key bits per raw key bit for the unbiased case. This represents an increase in the efficiency of the key generation rate by 79%.
We investigate a quantum key distribution (QKD) scheme which utilizes a biased basis choice in order to increase the efficiency of the scheme. The optimal bias between the two measurement bases, a more refined error analysis, and finite key size effects are all studied in order to assure the security of the final key generated with the system. We then implement the scheme in a local entangled QKD system that uses polarization entangled photon pairs to securely distribute the key. A 50/50 non-polarizing beamsplitter with different optical attenuators is used to simulate a variable beamsplitter in order to allow us to study the operation of the system for different biases. Over 6 hours of continuous operation with a total bias of 0.9837/0.0163 (Z/X), we were able to generate 0.4567 secure key bits per raw key bit as compared to 0.2550 secure key bits per raw key bit for the unbiased case. This represents an increase in the efficiency of the key generation rate by 79%.
We devise a simple modification that essentially doubles the efficiency of a well-known quantum key distribution scheme proposed by Bennett and Brassard (BB84). Our scheme assigns significantly different probabilities for the different polarization bases during both transmission and reception to reduce the fraction of discarded data. The actual probabilities used in the scheme are announced in public. As the number of transmitted signals increases, the efficiency of our scheme can be made to approach 100%. An eavesdropper may try to break such a scheme by eavesdropping mainly along the predominant basis. To defeat such an attack, we perform a refined analysis of accepted data: Instead of lumping all the accepted data together to estimate a single error rate, we separate the accepted data into various subsets according to the basis employed and estimate an error rate for each subset {\it individually}.
We devise a simple modification that essentially doubles the efficiency of a well-known quantum key distribution scheme proposed by Bennett and Brassard (BB84). Our scheme assigns significantly different probabilities for the different polarization bases during both transmission and reception to reduce the fraction of discarded data. The actual probabilities used in the scheme are announced in public. As the number of transmitted signals increases, the efficiency of our scheme can be made to approach 100%. An eavesdropper may try to break such a scheme by eavesdropping mainly along the predominant basis. To defeat such an attack, we perform a refined analysis of accepted data: Instead of lumping all the accepted data together to estimate a single error rate, we separate the accepted data into various subsets according to the basis employed and estimate an error rate for each subset individually.
This paper proposes a scheme for quantum cryptography with a nonmaximally entangled qubit pair. In a two-way configuration similar to quantum super dense coding, a two-bit key can be distributed by a round trip of one particle of the qubit pair and received by an appropriate joint measurement with the other. The security of our scheme is based on the quantum-mechanical impossibility of local unitary transformation between certain nonmaximally entangled states. Although an eavesdropper, Eve, can always identify the quantum state and intercept the key, it is impossible for her to resend the state with a unity probability and the legitimate parties inevitably detect her. Our protocol is also capable to quantum secure direct communication.