Entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures and mutually unbiased measurements
Shan Huang, Zeng‐Bing Chen, Shengjun Wu · Physical Review A · 2021
We construct inequalities between R\'enyi $\ensuremath{\alpha}$-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-POVMs) and mutually unbiased measurements (MUMs). 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.