Uncertainty reconciles complementarity with joint measurability

摘要

The fundamental principles of complementarity and uncertainty are shown to berelated to the possibility of joint unsharp measurements of pairs ofnoncommuting quantum observables. A new joint measurement scheme forcomplementary observables is proposed. The measured observables are representedas positive operator valued measures (POVMs), whose intrinsic fuzzinessparameters are found to satisfy an intriguing pay-off relation reflecting thecomplementarity. At the same time, this relation represents an instance of aHeisenberg uncertainty relation for measurement imprecisions. Amodel-independent consideration show that this uncertainty relation islogically connected with the joint measurability of the POVMs in question.