Imprecision Plateaus in Quantum Steering - Svegborn,Elna (2024)
In 1935, Schrödinger noted that if one of two entangled particles is subjected to a suitable measurement, it appears as if the state of the other particle is instantaneously influenced at a distance. This phenomenon, which Schrödinger referred to as quantum steering, exhibits properties favorable for quantum information theory. Therefore, much research has been put into developing criteria to detect quantum steering. In particular, to detect if an unknown state is so-called steerable, one must characterize the state by performing suitable measurements on it. Since quantum measurements cannot be implemented exactly, new steering criteria that take into account the lack of perfect measurement control have been developed in the last few years. However, the ability of these criteria to detect steering typically deteriorates rapidly as small measurement imprecisions are permitted in the analysis. In sharp contrast, a very different steering criterion was recently found through numerical analysis. Interestingly, this criterion suggests the existence of an "imprecision plateau", i.e., a limited regime in which imprecise measurements do not appear to influence the criterion's ability to detect quantum steering. The aim of this project is to explore this observation. In particular, this is done in a framework in which the experimenter can estimate how well the lab's measurements approximate the intended measurements. We start by analytically proving the existence of the described "imprecision plateau" for the Elegant Bell Inequality (EBI) steering scenario. Thereafter, we show that this phenomenon is not unique to the EBI scenario, but occurs in other steering scenarios as well. Finally, we investigate how numerical optimization methods that bound the set of quantum correlations from the interior and the exterior can be used to study the imprecision plateau in more complex settings.