Developing Quantum Advantage by Understanding the Paradoxical Aspects of Measurement in Quantum Systems

This project investigates measurement in quantum mechanics. In classical physics, looking at a system has no intrinsic effect on how it behaves — we can measure anything we wish without it affecting what we would see if we measured anything else, so long as we measure carefully enough. In quantum physics, however, certain variables in a system cannot be measured simultaneously, such that we obtain the values of both, error-free, with certainty. This measurement-incompatibility of certain pairs of (conjugate) variables is a key part of quantum mechanics (Heisenberg’s Uncertainty Principle). Unfortunately, these conjugate variables are often pairs we want to know simultaneously — for instance, the position and momentum of an electron, or the energy and the time-of-arrival of a photon at a detector. A trade-off exists: the more information we have about one variable, the less we can have about the other. Beyond this measurement disturbance, for some quantum systems, even treating incompatible variables as simultaneously having defined (measurement-independent) values leads to contradictions. The values of variables in systems with this property (contextuality) seemingly vary depending on the context in which they are measured, and combining inferences from the results of different measurements together leads to paradoxes. Because of this, contextual systems can possess combinations of properties which we would expect to be mutually contradictory. As well showing the peculiar nature of a quantum world, contextuality appears to be the key property which allows quantum computers an advantage over classical computers. This project considers the relationship between contextuality, quasiprobability negativity, and nonclassical measurement dynamics in genuinely quantum interactions. It involves identifying the meaning of negative quasiprobabilities (e.g., negative Kirkwood-Dirac distributions), and anomalous weak values; investigating how they link to contextuality; and applying the knowledge gained to help resolve key problems in quantum technologies, such as identifying the origin of, and learning how to leverage, quantum computational and metrological advantage to develop new quantum technologies. This research combines foundational questions regarding the paradoxical nature of quantum statistics with a search for more efficient applications of quantum resources, and for indicators to help us identify scenarios where there will be quantum advantage. It also links this theoretical work to experimental reality, fostering collaboration with experimental physicists, and identifying and demonstrating real technological benefits from the research. Worldwide, there is a race to develop useful quantum technologies. All quantum technologies were initially based on theoretical quantum foundational work. This illustrates how critically important quantum foundational research is, and why foundational work is necessary if we want to develop truly new quantum technologies (rather than just making short-term minor enhancements to current technologies). It is becoming increasingly apparent that we are facing difficulties developing new algorithms and approaches which provide quantum advantage. For instance, aside from classically-inspired and energy-minimisation algorithms, we only have two real useful quantum algorithms, Shor’s and Grover’s, both of which were found nearly thirty years ago. A reason for this thirty-year lack of progress in quantum algorithm development is that we do not yet understand well enough the fundamental aspects of quantum mechanics, such as contextuality, which underpin behaviours useful algorithms could leverage. Therefore, understanding contextuality is essential for us to harness quantum computing’s full potential. This project leverages foundations to pave the way for the novel quantum protocols, algorithms, and technologies of the future.