RS Fellow - EPSRC grant (2016): Investigating Measurement Incompatibility in Quantum Theory

量子理论中最著名的预言之一是海森堡的测不准原理，该原理认为，物体位置的不确定性乘以其动量的不确定性，从根本上受到限制，永远不会小于普朗克常数的一半，普朗克常数是自然界的基本常数之一。这是所谓的位置和动量测量不相容的显著结果之一，即在基本层面上，不可能设计出一种方法来同时测量物体的位置和动量。测量不相容是量子测量的一个普遍特征，也是量子理论的基本特征之一。它是一个完全背离经典物理学的地方。虽然表面上是一个限制，但它实际上开启了许多迷人的新效应的可能性，尤其是量子理论的非局部效应，即对一个系统的测量似乎会以一种违反经典解释的方式，瞬间影响到遥远的系统。在这个项目中，我计划研究一些关于测量不相容的迷人问题，这些问题仍然是开放的，特别是那些与这些测量可能产生的非局域性有关的问题，以及由量子信息理论引起的问题，在量子信息理论中，人们使用量子效应以经典不可能的方式处理信息。特别是，是否每一组不相容的测量都导致量子非定域性，或者是否需要测量的附加性质，这是一个基本的结构问题，仍然是未知的。此外，测量不相容在涉及多方的量子网络中所起的作用很少被探索，但从量子信息的角度来看是非常相关的。量子测量也必然会干扰被探测的系统。干扰量与不相容之间的关系尚不清楚，需要进一步调查。最后，即使测量在原则上是相容的，同时测量它们的方式也可能是极其复杂的。了解哪些兼容度量是最复杂的，或者如何设计不那么复杂的方法来度量它们是有趣的问题。回答这些令人着迷的问题肯定会提高我们对量子测量的理解，并为进一步的研究打开大门。

One of the most famous predictions of quantum theory is Heisenberg's uncertainty principle, which says that the uncertainty in the position of an object, multiplied by the uncertainty in its momentum, is fundamentally constrained, to never be smaller than half the reduced Planck constant, one of the fundamental constants of nature. This is one of the striking consequences of the so-called incompatibility of the measurements of position and momentum, that it is impossible, at a fundamental level, to ever devise a way to measure the position and the momentum of an object at the same time.Measurement incompatibility is a generic feature of quantum measurements, and one of the basic features of quantum theory. It is one of the places where a complete departure from classical physics occurs. Although seemingly a limitation, it in fact opens up the possibility of many fascinating new effects, not least the nonlocal effects of quantum theory, whereby measurements on one system seemingly affect - instantaneously - distant systems, in a way which defies classical explanation.In this project I plan to investigate some of the fascinating problems concerning measurement incompatibility that remain open, especially those which relate to the nonlocality that such measurements can generate, and questions motivated by quantum information theory, where one uses quantum effects to process information in ways which are impossible classically.In particular, it is still unknown if every set of incompatible measurements leads to quantum nonlocality, or if additional properties of the measurements are required, a basic structural question. Moreover, the role that measurement incompatibility plays in quantum networks involving many parties is little explored, but very relevant from a quantum information perspective. Quantum measurements also necessarily disturb the system being probed. How the amount of disturbance relates to incompatibility is not well understood, and warrants further investigation. Finally, even when measurements are in principle compatible, the way in which they can be measured simultaneously can be extremely complex. Understanding which compatible measurements are the most complicated, or how to devise less complex methods to measure them are interesting problems.Answering these fascinating questions will surely improve our understanding of quantum measurements, and open to door to further investigation.