开放二能级量子系统的对易关系保持性和物理可实现性
Preservation of Commutation Relations and Physical Realizability of Open Two-Level Quantum Systems
摘要：
相干反馈控制考虑纯粹的量子控制器，以克服缺点，如合适的量子信息的获取，量子纠错等，这些方法缺乏一个系统的表征量子可实现性。最近，当描述为线性随机微分方程的系统是量子时的一个条件被开发出来。这个条件被称为物理可实现性，它是针对满足量子谐振子正则对易关系的线性量子系统而提出的。在这种情况下，开放的二能级量子系统逃脱了当前已知条件的范围。与线性量子系统相比，获得此类系统的这种条件的挑战在于，发展方程现在是双线性量子随机微分方程，并且此类系统的对易关系依赖于系统变量。本文的目的是提供保泡利对易关系的一个充要条件，并阐明这个条件与物理可实现性之间的关系。
英文摘要：
Coherent feedback control considers purely quantum controllers in order to overcome disadvantages such as the acquisition of suitable quantum information, quantum error correction, etc. These approaches lack a systematic characterization of quantum realizability. Recently, a condition characterizing when a system described as a linear stochastic differential equation is quantum was developed. Such condition was named physical realizability, and it was developed for linear quantum systems satisfying the quantum harmonic oscillator canonical commutation relations. In this context, open two-level quantum systems escape the realm of the current known condition. When compared to linear quantum system, the challenges in obtaining such condition for such systems radicate in that the evolution equation is now a bilinear quantum stochastic differential equation and that the commutation relations for such systems are dependent on the system variables. The goal of this paper is to provide a necessary and sufficient condition for the preservation of the Pauli commutation relations, as well as to make explicit the relationship between this condition and physical realizability.
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