Entropic uncertainty relations for SIC-POVMs and MUMs

Abstract

We construct inequalities between Rényi 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.

References in corpus (3)

• Entropic uncertainty relation for mutually unbiased bases
• Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases
• Symmetric Informationally Complete Measurements of Arbitrary Rank

Cited by in corpus (1)

• Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis