Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

Bilal Canturk, Zafer Gedik

Published 2020-01-31Version 1

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 have pointed out the fact that our result provides a quantitative criterion for the extendable of MUBs. In addition, we have applied our result to the mutual information of $d+1$ observables conditioned with a classical memory.