Entropic uncertainty relations for SIC-POVMs and MUMs

• URL: http://arxiv.org/abs/2011.00808v3
• Date: Mon, 12 Apr 2021 03:43:10 GMT
• Title: Entropic uncertainty relations for SIC-POVMs and MUMs
• Authors: Shan Huang, Zeng-Bing Chen, and Shengjun Wu
• Abstract summary: We construct inequalities between R'enyi entropy and the indexes of coincidence of probability distributions. We show that our uncertainty relations for general SIC-POVMs and MUMs can be tight for sufficiently mixed states.
• Score: 3.1192220661407526
• License: http://creativecommons.org/licenses/by/4.0/
• 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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