Unsharp Measurements and Joint Measurability

摘要: We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). exemplify the role played by measurability POVMs in entropic uncertainty relation for Alice’s pair non-commuting observables presence Bob’s entangled quantum memory. show that Bob should record the outcomes incompatible (non-jointly measurable) POVMs his quantum memory so as to beat bound. In other words, addition to Alice–Bob state, implementing incompatible at end is necessary to uncertainty bound and hence predict the outcomes with improved precision. also explore implications of validate a moment matrix constructed from average pairwise correlations of three dichotomic qubit observables. We prove classically acceptable matrix – which ascertains existence legitimate joint probability distribution all the three – could be realized if and only if compatible are employed.