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Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases

Manuel A. Ballester·Stephanie Wehner
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Abstract

We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink for 2 such measurements can in fact be tight for up to sqrt{d} measurements in mutually unbiased bases. We then show that using more mutually unbiased bases does not always lead to a better locking effect. We prove that the optimal bound for the accessible information using up to sqrt{d} specific mutually unbiased bases is log d/2, which is the same as can be achieved by using only two bases. Our result indicates that merely using mutually unbiased bases is not sufficient to achieve a strong locking effect, and we need to look for additional properties.

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Manuel A. Ballester, Stephanie Wehner. 2007-03-21. Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases. https://doi.org/10.1103/physreva.75.022319

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