用结构物理近似设计量子信息处理
Designing Quantum Information Processing via Structural Physical Approximation
摘要：
在量子信息处理中，有可能具有超越经典系统的限制的高效计算和安全通信。然而，从基本的观点来看，由量子力学定律演化出的量子系统比经典系统更具限制性，它被确定为一种特定形式的动力学，即幺正变换，因此，它是到子系统的正映射和完全正映射。这也表征了量子系统上不允许的变换的类别，其中正的但不完全的映射是特别感兴趣的，因为它们表征了纠缠态，这是量子信息处理中的一般资源。结构物理近似提供了一种系统的方法，用量子信道来近似那些非物理映射，正的但不完全正的映射。自从它作为一种探测纠缠态的方法被提出以来，它激发了正映射的分类、厄米算符和量子态的结构以及量子测量（如量子信息理论中的量子设计）等基本问题。在实践中，它已经发展出了直接探测纠缠态的有效可行的方法，并利用光子量子比特态进行了原理验证实验。本文综述了结构物理近似下的量子信息处理及其研究进展。本文主要介绍结构物理近似的性质及其在实际信息应用中的应用。
英文摘要：
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.
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