基于量子系统与路径探测器纠缠的波－粒互补性的研究对深入理解玻尔互补原理、量子干涉及纠缠等量子力学基本原理及概念具有重要意义。本项目拟对这个课题进行系统性研究。和已有研究不同的是，我们侧重研究系统干涉条纹可见度及可获得的路径信息与系统－路径探测器纠缠度的定量关系，并基于路径探测器的相干叠加性提出量子延迟选择试验。我们将首先研究一个量子比特充当干涉比特的路径探测器的情况，探讨干涉条纹可见度及路径信息对两个比特纠缠度的依赖关系。然后在腔QED系统中提出相应物理过程的实现方案，并研究退相干效应对所导致的修正。将结果进行推广，研究路径探测器为连续变量系统的情形。进一步研究路径探测器处于“在”与“不在”相干叠加的情况，提出基于这种相干叠加性的量子延迟选择实验，并在腔QED系统中设计出具体方案以实现相应物理过程。最后研究路径探测器的退相干效应对干涉条纹恢复的影响。

Investigation of the wave-particle complementarity based on the entanglement between a quantum system and a which-path detector is important for deeply understanding the fundamental principles and concepts of quantum mechanics, such as Bohr’s complementarity principle, quantum interference, and entanglement. In this project, we plan to systematically study this topic. In contrast with previous studies, we will focus on the quantitative relations of the visibility of the system’s interference fringes and of the amount of available path information to the degree of entanglement between the system and the which-path detector, and propose the quantum delayed-choice experiment based on the coherent superposition of the which-path detector. First we will study the case where one qubit acts as the which-path detector of the interfering qubit, and explore the dependences of the interference fringe visibility and amount of the available path information on the entanglement between these two qubits. Then we will propose schemes for implementation of the corresponding physical processes in cavity QED systems, and study the corrections caused by decoherence effects. Next, we will generalize the results, studying the case that the which-path detector is a continuous-variable system. We further investigate the case where the which-path detector is in a superposition of the “present” and “absent” states, propose a quantum delayed-choice experiment based on such a coherent superposition state, and present schemes to implement the corresponding physical process in cavity QED systems. Finally, we will explore the effect of decoherence of the which-path detector on the restoration of the interference fringes.