Limits on entropic uncertainty relations for 3 and more MUBs

Authors:
Andris Ambainis
Affiliations:
Faculty of Computing, University of Latvia, Latvia
Venue:
Quantum Information & Computation
Year:
2010

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Abstract

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