Apparent suppression of quantum observable conjugacy through joint weak measurements

Abstract

We use a measurement scheme of simultaneously coupling two meters to one system, wherein each meter probes an observable and the other meter measures the corresponding conjugate observable. In the process, we note an effect of the explicit coupling strength which seemingly suppress the conjugacy of both observables. That happens in a case we call very weak measurement such that the contributions of the commutator terms of the evolution operator describing the measurement are considerably small.