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

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.

9 pages, RevTeX, v3: complete rewrite, new title, many new results, v4: minor changes, published version

References in corpus (3)

• Randomizing quantum states: Constructions and applications
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Security of quantum bit string commitment depends on the information measure

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• Higher entropic uncertainty relations for anti-commuting observables
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• Variations on a theme of Heisenberg, Pauli and Weyl
• Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra
• Cryptography in a Quantum World
• Complementarity of information sent via different bases