Limits on entropic uncertainty relations for 3 and more MUBs

Details Limits on entropic uncertainty relations for 3 and more MUBs Limits on entropic uncertainty relations for 3 and more MUBs

2009-09-21

arxiv.org/abs/0909.3720v2

Physics

Quantum Physics

11 pages, many small corrections, this version to appear in QIC

Scientific paper

We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3 MUBs and at least one choice of a larger number of MUBs, the best possible entropic uncertainty relation can be only marginally better than the one that trivially follows from the relation by Maassen and Uffink (PRL, 1987) for 2 bases.

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