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Tight entropic uncertainty relations for systems with dimension three to five

2017/01/16 by Alberto Riccardi, Chiara Macchiavello, Lorenzo Maccone · 1 citation
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.95.032109

published as Phys. Rev. A 95, 032109 (2017)

arxiv created 2017/01/16 · arxiv updated 2017/03/15

Abstract

We consider two (natural) families of observables Ok for systems with dimension d=3,4,5: the spin observables Sx, Sy and Sz, and the observables that have mutually unbiased bases as eigenstates. We derive tight entropic uncertainty relations for these families, in the form ∑kH(Ok)\geqslantαd, where H(Ok) is the Shannon entropy of the measurement outcomes of Ok and αd is a constant. We show that most of our bounds are stronger than previously known ones. We also give the form of the states that attain these inequalities.

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