Incompatibility in Quantum Parameter Estimation

TL;DR

This paper introduces a geometric measure of quantum incompatibility in multi-parameter estimation, analyzes its behavior under noise, and provides computational tools and models for compatible quantum systems.

Contribution

It proposes a new measure of quantum incompatibility with operational meaning, and develops numerical methods to evaluate and understand it in practical scenarios.

Findings

The measure captures the effect of noise on quantum incompatibility.

A semidefinite program enables numerical computation of the measure.

Compatible models can be constructed for certain unitary encodings.

Abstract

In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some simple systems in order to track the effect of a local depolarizing noise on the incompatibility of the estimation task. A semidefinite program is described and used to numerically compute the figure of merit when the analytical tools are not sufficient, among these we include an upper bound computable from the symmetric logarithmic derivatives only. Finally we discuss how to obtain compatible models for a general unitary encoding on a finite dimensional probe.