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

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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.