Robustness of incompatibility for quantum devices

TL;DR

This paper introduces a robustness measure for quantum device incompatibility, extending convex geometry concepts, and calculates it for specific pairs of quantum devices, enhancing understanding of quantum incompatibility quantification.

Contribution

It proposes a new robustness measure for quantum incompatibility and applies it to specific cases, bridging convex geometry and quantum information theory.

Findings

Robustness measure for quantum incompatibility is defined.

Calculated robustness for Fourier-coupled observables, decodable channels, and their combinations.

Abstract

A robustness measure for incompatibility of quantum devices in the lines of the robustness of entanglement is proposed. The concept of general robustness measures is first introduced in general convex-geometric settings and these ideas are then applied to measure how incompatible a given pair of quantum devices is. The robustness of quantum incompatibility is calculated in three special cases: a pair of Fourier-coupled rank-1 sharp observables, a pair of decodable channels, where decodability means left-invertibility by a channel, and a pair consisting of a rank-1 sharp observable and a decodable channel.