Incompatibility Robustness of Quantum Measurements: A Unified Framework
July 29th, 2019 MATÉ FARKAS Université Gdansk

One might be tempted to argue that the most important distinction between classical theories and quantum mechanics is the way we model the act of performing a measurement. Classically, a measurement process corresponds to simply revealing an unknown (but pre-existing) value, which leaves the state of the system untouched. In quantum mechanics, on the other hand, performing a measurement is an active and invasive process which (in most cases) disturbs the system. This implies that there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. Although several measures have been proposed to quantify how incompatible a set of measurements is, their properties are not well understood. In this work we propose several conditions that a reasonable measure of incompatibility should satisfy and we investigate whether the existing measures comply with those. Quite surprisingly we find that some of the widely used measures do not fulfil these basic requirements. Moreover, we show that when looking for the most incompatible pair of quantum measurements we obtain different (often counter-intuitive) answers depending on the exact measure. This means that we are still far from understanding how to measure the incompatibility of quantum measurements in a meaningful manner.

Seminar, July 29, 2019, 12:00. ICFO’s Seminar Room

Hosted by Prof. Antonio Acín