Department of Applied Mathematics, Hanyang University (ERICA), 55 Hanyangdaehak-ro, Ansan, Gyeonggi-do, 426-791, Republic of Korea. Freiburg Institute for Advanced Studies (FRIAS), Albert-Ludwigs University of Freiburg, Albertstrasse 19, 79104 Freiburg, Germany.
Rep Prog Phys. 2017 Oct;80(10):104001. doi: 10.1088/1361-6633/aa7d45. Epub 2017 Jul 4.
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.
在量子信息处理中，有可能超越经典系统的限制，实现高效计算和安全通信。然而，从量子力学定律的角度来看，量子系统的演化比经典系统更具限制性，经典系统被确定为特定形式的动力学，即幺正变换，因此对子系统的正变换和完全正变换。这也刻画了量子系统中禁止的变换类，其中正但非完全正的变换特别有趣，因为它们刻画了纠缠态，这是量子信息处理中的一般资源。结构物理逼近提供了一种系统的方法来用量子信道逼近那些非物理的映射，即正但非完全正的映射。由于它被提议作为一种检测纠缠态的方法，它激发了关于正映射的分类以及厄米算子和量子态的结构、以及量子测量（如量子信息论中的量子设计）的基本问题。它已经开发出了有效的、可行的直接检测纠缠态的方法，其实验证明也已经在光子量子位态上进行了。在这里，我们对结构物理逼近及其相关进展进行了全面的综述。该综述主要集中在结构物理逼近的性质及其在实际信息应用中的应用。
