基于广义测量的多体量子态self-test的实验研究

量子态识别在量子通信中有着重要的应用，随着希尔伯特空间维度的扩张，对量子态的准确识别越来越复杂和困难。Self-test是一种基于非局域性判据，对量子态执行少量测量推断目标量子态类型的方法。本项目通过将广义测量引入量子导引不等式，理论推导和实验验证新型多体量子态self-test方案，解决少量拷贝情况下如何准确识别多体量子态的关键问题。主要内容包括:（1）将广义测量代替投影测量，研究新型的多体量子导引不等式，通过构建局域等距映射，推导基于广义测量的多体量子态self-test方案；（2）结合量子行走模型，实验上利用线性光学体系实现任意二维和高维广义测量算子，搭建普适广义测量装置；（3）利用线性光学体系实现基于广义测量的多体量子态self-test方案。对self-test方案进行鲁棒性分析，探究新型多体量子态self-test方案在噪声环境下的适用情况，为实际多体量子态识别提供实验基础。

Quantum state discrimination has important applications in quantum communication. However, it becomes more and more complicated and difficult to discriminate quantum states with the expansion of Hilbert space. Self-test is a method to infer the type of the target quantum states through performing a small amount of measurement based on non-local criteria. This project theoretically and experimentally demonstrates a new multi-partite quantum state self-test scheme by introducing the generalized measurement into quantum steering inequalities, which solves the key problem of how to accurately identify the multi-partite quantum state with a small number of copies. Firstly, by replacing generalized measurement with projection measurement, we study a new type of multi-partite quantum steering inequalities, and construct a local isometry to derive a multi-partite quantum state self-test scheme based on generalized measurement. Secondly, we experimentally realize arbitrary two and high-dimensional generalized measurement operators via the quantum walk by using linear optical system and build a universal generalized measurement device. Finally, we experimentally implement the new multi-partite quantum state self-test scheme based on generalized measurement. We explore the applicability of the new multi-partite quantum state self-test scheme in a noisy environment by the robustness analysis in order to provide an experimental basis for the actual multi-partite quantum state discrimination.