Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The paper investigates the optimal upper bound of entropic uncertainty relation for N Mutually Unbiased Bases (MUBs) and provides a quantitative criterion for the extendibility of MUBs based on entropic certainty relation. The results are also applied to the information exclusion relation of (d+1) observables conditioned with a classical memory to detect the compatibility of the observables.