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arXiv · 2011.00808

Entropic uncertainty relations for SIC-POVMs and MUMs

Shan Huang·Zeng-Bing Chen·Shengjun Wu
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Abstract

We construct inequalities between R\'{e}nyi entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures (SIC-POVM) and mutually unbiased measurements (MUM) on finite dimensional systems. We show that our uncertainty relations for general SIC-POVMs and MUMs can be tight for sufficiently mixed states, and moreover, comparisons to the numerically optimal results are made via information diagrams.

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Shan Huang, Zeng-Bing Chen, Shengjun Wu. 2020-11-02. Entropic uncertainty relations for SIC-POVMs and MUMs. https://doi.org/10.1103/physreva.103.042205

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