基于局域操作与经典通信的量子状态区分及相关问题的研究

Quantum state discrimination based on local operations and classical communications (LOCC), is the basic problem in the field of quantum information. Study on quantum states LOCC discrimination, maybe help us to deepen the understanding of quantum non-locality, and also to promote sovling the other basic issues associated with quantum non-locality property. This project aims to research quantum mixed state LOCC unambiguous discrimination and unknown pure states LOCC unambiguous identification. The detail contents are as follows: (1) Based on the research in LOCC realizability of POVM measurement, we aim to investigate whether LOCC unambiguous discrimination can reach the optimal efficiency as global operation discrimination. Using some important characteristics of measurement operator in unambiguous discrimination, combined with mathematical calculation skills, we aim to propose a bound on the maximum successs probability of LOCC unambiguous discrimination between quantum mixed states. (2) Proposed by the definition of average density operator, combined with the completeness and the interaction characteristics of the measurement operator, using some arithmetical techniques, we aim to research the equality between unknown pure states LOCC identification and quantum mixed state LOCC discrimination. Moreover, we will further study the bound of the maximum success probability of unknown pure states LOCC identification. These results will be helpful for further research on quantum communication, and the other basic issues associated with quantum non-locality property.

基于局域操作与经典通信（LOCC）的量子状态区分,是量子信息领域中的一个基本问题。研究量子态的LOCC区分，有助于加深对量子非局域性的理解，同时也可推动与量子非局域性有关的其它基本问题的研究。本项目拟对量子混合态LOCC无歧区分和未知纯态LOCC无歧识别进行研究，具体内容为:(1)在研究POVM测量的LOCC可实现性的基础上，探讨LOCC区分能否达到全局操作的最优区分效率；利用无歧区分测量算子的一些重要特性，结合数学运算技巧，研究量子混合态LOCC无歧区分最大成功概率的界；(2)拟通过定义平均密度算子，结合测量算子的完备性和相互制约的特性，利用数学推导技巧，来研究未知纯态的LOCC识别与量子混合态LOCC区分的等价性问题，并给出量子未知纯态LOCC无歧区分最大成功概率的界。本项目的研究结果将为进一步研究量子通信以及与量子非局域性有关的其它基本问题提供帮助。