2009/09/21 by Andris Ambainis, Ambainis, Andris
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.0909.3720
11 pages, many small corrections, this version to appear in QIC
arxiv created 2010/07/16 · arxiv updated 2010/07/19
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.