Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

• URL: http://arxiv.org/abs/2002.00004v2
• Date: Thu, 6 Feb 2020 12:56:23 GMT
• Title: Optimal upper bound of entropic uncertainty relation for mutually unbiased bases
• Authors: Bilal Canturk and Zafer Gedik
• Abstract summary: We have obtained the optimal upper bound of entropic uncertainty relation for $N$ Mutually Unbiased Bases (MUBs) Our result is valid for any state when $N$ is $d+1$, where $d$ is the dimension of the related system.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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