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arXiv · 2002.00004

Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

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

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Bilal Canturk, Zafer Gedik. 2020-02-06. Optimal upper bound of entropic uncertainty relation for mutually unbiased bases. https://doi.org/10.1016/j.physa.2021.126275

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