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Physical Review A

Quantum channel capacity by simulated annealing

Frederick H. Willeboordse, Ajay Gopinathan, Dagomir Kaszlikowski

Published Apr 5, 2005• 3 citations
Publisher

Abstract

It is shown how simulated annealing can be used to determine the accessible information and the capacity of a quantum channel. The method is applied to a specific example of a symmetric $N$-state quantum channel that frequently appears in the analysis of eavesdropping in quantum key distribution protocols. The numerical results for the accessible information of this quantum channel are compared with recently published analytical solutions showing excellent agreement. Furthermore, interesting results concerning the capacity of a symmetric quantum channel are presented.

DOI
10.1103/physreva.71.042310

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It is shown how simulated annealing can be used to determine the accessible information and the capacity of a quantum channel. The method is applied to a specific example of a symmetric NNN-state quantum channel that frequently appears in the analysis of eavesdropping in quantum key distribution protocols. The numerical results for the accessible information of this quantum channel are compared with recently published analytical solutions showing excellent agreement. Furthermore, interesting results concerning the capacity of a symmetric quantum channel are presented.
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Quantum key distribution (QKD) enables secure information exchange with untrusted quantum links between remote communication parties. A central task in the studies of QKD protocols is security analysis, which aims at deriving the length of the final key such that it is secure regardless of the eavesdropper's computational power. In literature, the security analysis has been done both analytically and numerically. Compared to analytical methods which tend to require techniques specific to each QKD protocol, numerical ones are more general since they can be directly applied to many QKD protocols with little adaptation. However, current numerical methods are carried out based on some assumptions such as working in the asymptotic limit and collective attacks from eavesdroppers. In this work, we remove these assumptions and develop a numerical finite-size security analysis against general attacks for a large class of QKD protocols. We also give an example of applying the method to the recent phase-matching QKD protocol with a simplified protocol design. Our result shows that the finite-size key rate can surpass the linear key-rate bound with a practical QKD system operated for only several hours.
This paper presents a comprehensive analysis of the channel capacity for Quantum Key Distribution (QKD) channels. The core aim is to provide a rigorous theoretical framework for understanding and optimizing QKD systems, ultimately guiding their practical implementation. We leverage principles from quantum information theory to quantify the information transmission capabilities within a QKD channel. This analysis considers various factors including quantum noise, channel loss, and the specific QKD protocol employed. The results contribute to a deeper understanding of the fundamental limits of QKD and offer valuable insights for designing more robust and efficient quantum key distribution systems. We define channel capacity as *C* where *C* = *I(X;Y)*, with *I(X;Y)* representing the mutual information between the input qubits *X* and the output qubits *Y*. The theoretical framework presented here will be instrumental in future research and development within the field of quantum cryptography.
Quantum key distribution (QKD) allows the transmission of keys with unconditional security. Nevertheless, a discrepancy remains between the theoretical framework and the practical implementation, as device imperfections are frequently neglected in most QKD protocols. Some previous works proposed to use Hong-Ou-Mandel interference to quantify information leakage from side-channels. However, the security bound was relatively loose, resulting in poor performance. In this paper, we present an improved method for the security analysis of practical QKD protocols and provide a more precise parameter estimation. Furthermore, we apply it to several important QKD protocols, including BB84, measurement-device-independent, and twin-field, and carry out corresponding numerical simulations. Our work demonstrates significant improvements in both the key rate and the transmission distance compared to previous methods, representing a crucial step towards the practical implementation of QKD.