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Journal of Software

基于量子Calderbank-Shor-Steane纠错码的量子安全直接通信

吕欣, 马智, 冯登国

Published Jan 1, 2006• 0 citations

Abstract

量子安全直接通信是继量子密钥分配之后提出的又一重要量子密码协议，它要求通信双方在预先不需要建立共享密钥的情况下就可以实现消息的保密传输．给出了一个新的量子安全直接通信方案，该方案利用量子Calderbank-Shor-Steane（CSS）纠错码和未知量子态不可克隆等性质，方案的安全性建立在求解一般的线性码的译码问题是一个NP完全问题、Goppa码有快速的译码算法和量子图灵机不能有效求解NP完全问题的基础上．在协议中，发送方Alice把要发送的秘密消息转化为一一对应的错误向量。把错误向量加到其接收到的、Bob编码过的量子态上，并发给接收方Bob．Bob利用其私钥，通过测量、解码可以得到错误向量，并可以用相应的算法恢复出秘密消息．控制量子信道的攻击者Eve不能恢复出秘密消息，因其不知道Bob的密钥．一与已有的量子安全直接通信方案相比，该方案不需要交换任何额外的经典信息和建立量子纠缠信道．

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量子安全直接通信是继量子密钥分配之后提出的又一重要量子密码协议，它要求通信双方在预先不需要建立共享密钥的情况下就可以实现消息的保密传输．给出了一个新的量子安全直接通信方案，该方案利用量子Calderbank-Shor-Steane（CSS）纠错码和未知量子态不可克隆等性质，方案的安全性建立在求解一般的线性码的译码问题是一个NP完全问题、Goppa码有快速的译码算法和量子图灵机不能有效求解NP完全问题的基础上．在协议中，发送方Alice把要发送的秘密消息转化为一一对应的错误向量。把错误向量加到其接收到的、Bob编码过的量子态上，并发给接收方Bob．Bob利用其私钥，通过测量、解码可以得到错误向量，并可以用相应的算法恢复出秘密消息．控制量子信道的攻击者Eve不能恢复出秘密消息，因其不知道Bob的密钥．一与已有的量子安全直接通信方案相比，该方案不需要交换任何额外的经典信息和建立量子纠缠信道．

We expand the class of holographic quantum error-correcting codes by developing the notion of block perfect tensors, a wider class that includes previously defined perfect tensors. The relaxation of this constraint opens up a range of other holographic codes. We demonstrate this by introducing the self-dual Calderbank-Shor-Steane (CSS) heptagon holographic code, based on the 7-qubit Steane code. Finally, we show promising thresholds for the erasure channel by applying a straightforward, optimal erasure decoder to the heptagon code and benchmark it against existing holographic codes.

Shor and Steane ancilla are two well-known methods for fault-tolerant logical measurements, which are successful on small codes and their concatenations. On large quantum low-density-parity-check (LDPC) codes, however, Shor and Steane measurements have impractical time and space overhead respectively. In this work, we widen the choice of ancilla codes by unifying Shor and Steane measurements into a single framework, called homomorphic measurements. For any Calderbank-Shor-Steane (CSS) code with the appropriate ancilla code, one can avoid repetitive measurements or complicated ancilla state preparation procedures such as distillation, which overcomes the difficulties of both Shor and Steane methods. As an example, we utilize the theory of covering spaces to construct homomorphic measurement protocols for arbitrary

X

- or

Z

-type logical Pauli operators on surface codes in general, including the toric code and hyperbolic surface codes. Conventional surface code decoders, such as minimum-weight perfect matching, can be directly applied to our constructions.

信息安全一直是通信领域中的一个重要挑战，而密码通信是确保信息安全的关键。传统的经典密码通信方法在过去几十年中取得了巨大的进展，但也面临着越来越严重的安全挑战，尤其是在量子计算机的崭露头角下。为了应对这些挑战，量子密码通信作为一门新兴的领域正在快速发展，利用量子力学的原理来提供前所未有的安全性。本篇文章讨论了经典密码通信与量子密码通信的现状，以及分析未来的发展趋势，量子密码通信作为信息安全的未来方向，将提供更高级别的保障，以确保隐私和数据的安全传输。

量子纠缠叩开了量子精密测量精度突破标准量子极限的大门，当初始探针中的粒子态使用非经典资源时，量子精密测量精度能够逼近海森堡极限，显著提升测量的灵敏度。量子纠缠已在冷原子、囚禁离子和热原子等量子系统中展现出突破标准量子极限的强大潜力，有望推动物理学前沿发展和技术的创新进步。本文阐述量子纠缠增强量子精密测量领域的理论框架、纠缠对于测量的影响、纠缠态制备机理及量子传感器前沿应用。最后，对该领域进行了总结和展望。

Quantum low-density parity check (QLDPC) codes have rapidly developed in the field of quantum error correction in recent years. A variety of quantum code families have emerged from numerous research activities. In this paper, we employ concatenated Calderbank-Shor-Steane (CSS) codes, hypergraph product codes, and Bacon-Shor codes to train belief-propagation (BP) and neural BP (NBP) decoders. At the same time, we employ a concatenation scheme in BP and NBP, the amplified construction of CSS codes is realized, and the training of longer length parameter quantum codes is realized. The numerical results show that the concatenated CSS codes demonstrate better error correction performance compared to both hypergraph product codes and Bacon-Shor codes. In addition, the concatenated CSS codes are trained using the concatenation scheme to improve the error correction performance of the decoder.