普适的量子不确定关系的实验研究

量子不确定性是量子体系区别于经典体系的重要属性之一，在量子信息技术的发展中扮演了重要角色，因此从提出到现在一直是量子物理前沿理论和实验的研究热点之一。基于方差和熵的不确定关系被广泛研究的同时，采用受控（majorization）的概念刻画量子不确定性被提出，该方法可以将不确定关系推广到更普适的情况。根据数学形式的不同可分为直积受控不确定关系和直和受控不确定关系，两者的数学区别和在探测量子关联方面的应用受到广泛关注，但两者蕴含的物理本质区别仍然是未知的。本项目拟在实验上研究两种普适的受控不确定关系的物理本质区别。此外，量子不确定关系对于所有的量子态并没有给出一个全面的描述，如何构建量子不确定性区域给出量子不确定性的普适描述是该领域的研究重点和难点。本项目拟采用受控的方法研究可观测量之间的普适量子不确定性区域，并且分别探究二维系统和三维系统的量子不确定性区域的对称性问题。

Quantum uncertainty is one of the important properties of quantum system different from classical system and plays an important role in the development of quantum information technology. Therefore, it has been a hot topic in the research of frontier theory and experiment of quantum physics since it was proposed. While the uncertainty relation based on variance and entropy is widely studied, majorization is proposed to characterize the quantum uncertainty. This method can generalize the uncertainty relation. According to the different mathematical forms, it can be divided into direct-product majorization uncertainty relation and direct-sum majorization uncertainty relation. The mathematical difference between them and their application in detecting quantum correlation are widely concerned, but the physical essence difference between them is still unknown. This project plans to study the physical essence difference between two kinds of majorization uncertainty relations in experiment. Moreover, the quantum uncertainty relation does not give a comprehensive description of all quantum states. How to construct the quantum uncertainty region and give a universal description of quantum uncertainty is still the focus and difficulty in this field. In this project, we plan to use majorization to experimentally study the universal uncertainty region between different observables, and respectively explore the symmetry of the quantum uncertainty region in two-dimensional quantum system and three-dimensional quantum system.