Title:	Unsharp measurements and joint measurability
Authors:	Karthik, H.S. Usha Devi, A.R. Rajagopal, A.K.
Issue Date:	Dec-2015
Publisher:	Indian Academy of Sciences, Bangalore, India.
Citation:	Current Science, 2015, Vol.109, p2061
Abstract:	We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair of non-commuting observables in the presence of Bob's entangled quantum memory. We show that Bob should record the outcomes of incompatible (non-jointly measurable) POVMs in his quantum memory so as to beat the entropic uncertainty bound. In other words, in addition to the presence of entangled Alice-Bob state, implementing incompatible POVMs at Bob's end is necessary to beat the uncertainty bound and hence, predict the outcomes of non-commuting observables with improved precision. We also explore the implications of joint measurability to {\em validate} a moment matrix constructed from average pairwise correlations of three dichotomic non-commuting qubit observables. We prove that a classically acceptable moment matrix -- which ascertains the existence of a legitimate joint probability distribution for the outcomes of all the three dichotomic observables -- could be realized if and only if compatible POVMs are employed.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6415
ISSN:	0011-3891
Alternative Location:	http://arxiv.org/abs/1505.04246
Copyright:	2015 Indian Academy of Sciences
Appears in Collections:	Research Papers (LAMP)

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