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)≥αd, 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.

Tight entropic uncertainty relations for systems with dimension three to five

RICCARDI, ALBERTO;MACCHIAVELLO, CHIARA;MACCONE, LORENZO
2017-01-01

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)≥αd, 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1177025
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