Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

Official URL: https://arxiv.org/abs/2002.00004v2

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 extendibilty of MUBs. In addition, we have applied our result to the mutual information of d+1 observables conditioned with a classical memory.