非厄米哈密顿量子力学与开放系统理论之关系探究

In the conventional quantum mechanics, the Hamiltonian of a quantum system is a Hermitian operator. Since 1998, a new research field gradually emerged, which sometimes is called non-Hermitian-Hamiltonian quantum mechanics. Non-Hermitian-Hamiltonian quantum mechanics explores the question: how to use non-Hermitian Hamiltonians to describe quantum systems. So far more than ten times of international conferences about this topic have been held, meanwhile domestic researches for this topic are very lacking. This project will investigate the relationship between the theory of quantum open systems and the non-Hermitian-Hamiltonian quantum mechanics,i.e., how to use non-Hermitian Hamiltonians to equivalently express the theory of quantum open systems. Specifically, we will seek for appropriate non-Hermitian Hamiltonians, appropriate metric operators, and also perhaps appropriate complex contours, to equivalently express the basic equations, Lindblad equation and Kraus superoperator equation. Under this framework, we will also study some concrete open systems which are important in quantum information processing. With rapid progress of quantum information science, more and more open systems are desirable to be understood and controlled, the development of the open systems theory is therefore very demanded. So the results of this project are expected to be of important theoretical and practical values.

自1998年以来，国际物理学界开始研究如何用非厄米哈密顿来刻画量子系统。本项目将探究量子开放系统理论和非厄米哈密顿之间的关系。同时我们也将用非厄米哈密顿的方法来研究某些具体的量子开放系统。考虑到目前量子信息学的飞速发展对于量子开放系统理论的迫切需求，本项目的研究结果将具有重要的理论和应用价值。

在本项目执行的一年中（2014.1.1-2014.12.31），本项目组取得了若干研究成果（一篇研究论文已被International Journal of Theoretical Physics杂志（SCI）接收，即将发表；另有一篇研究论文正在审稿中）。这些成果未完成本项目的全部预设研究目标，但是对本项目预设目标的全部完成具有重要意义。