Entropic uncertainty relations and locking: Tight bounds for mutually unbiased bases
- Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands (Netherlands)
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 [Phys. Rev. Lett. 60, 1103 (1988)] for two such measurements can in fact be tight for up to {radical}(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 {radical}(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.
- OSTI ID:
- 20982086
- Journal Information:
- Physical Review. A, Vol. 75, Issue 2; Other Information: DOI: 10.1103/PhysRevA.75.022319; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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