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Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

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  • Canturk, Bilal
  • Gedik, Zafer

Abstract

We have obtained the optimal upper bound of entropic uncertainty relation for N Mutually Unbiased Bases (MUBs). We have used the methods of variational calculus for the states that can be written in terms of N MUBs. Our result is valid for any state when N is d+1, where d is the dimension of the related system. We provide a quantitative criterion for the extendibility of MUBs based on entropic certainty relation. In addition, we have applied our result to information exclusion relation of (d+1) observables conditioned with a classical memory which can be used to detect the compatibility of the observables.

Suggested Citation

  • Canturk, Bilal & Gedik, Zafer, 2021. "Optimal upper bound of entropic uncertainty relation for mutually unbiased bases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    • Handle: RePEc:eee:phsmap:v:582:y:2021:i:c:s0378437121005483
    DOI: 10.1016/j.physa.2021.126275
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