R\'enyi and Tsallis formulations of noise-disturbance trade-off relations

TL;DR

This paper develops new information-theoretic measures of noise and disturbance in quantum measurements using Rényi and Tsallis entropies, and derives related uncertainty trade-off relations.

Contribution

It introduces novel noise-disturbance measures based on conditional Rényi and Tsallis entropies and establishes corresponding uncertainty relations.

Findings

New measures of noise and disturbance using Rényi and Tsallis entropies

Derivation of noise-disturbance trade-off relations

Discussion of properties of conditional entropies in quantum measurements

Abstract

We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R\'{e}nyi and Tsallis entropies. Related information-theoretic measures of noise and disturbance are introduced. These definitions are based on the concept of conditional entropy. To motivate introduced measures, some important properties of the conditional R\'{e}nyi and Tsallis entropies are discussed. There exist several formulations of entropic uncertainty relations for a pair of observables. Trade-off relations for noise and disturbance are derived on the base of known formulations of such a kind.