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http://hdl.handle.net/2289/6415
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) |
Files in This Item:
File | Description | Size | Format | |
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2015_CS_109_2061.pdf | Open Access | 337.03 kB | Adobe PDF | View/Open |
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