Uncertainty relations based on mutually unbiased measurements

TL;DR

This paper establishes new uncertainty relations based on mutually unbiased measurements, providing both state-dependent and independent entropic bounds, and extends these relations to Rényi and Tsallis entropies.

Contribution

It introduces novel uncertainty inequalities for MUMs, including bounds in various entropy forms, advancing the theoretical understanding of measurement uncertainty.

Findings

Derived state-dependent and independent entropic bounds for MUMs

Formulated uncertainty relations using Rényi and Tsallis entropies

Extended uncertainty principles to mutually unbiased measurements in quantum systems

Abstract

We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by $d+1$ MUMs on any density operator $\rho$ in $\mathbb{C}^{d}$, both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of R\'{e}nyi and Tsallis entropies.