Dynamical resource theory of incompatibility preservability

TL;DR

This paper develops a new resource theory to quantify how well noisy quantum dynamics can preserve measurement incompatibility, a key quantum feature, using a robustness measure and an operational filter game.

Contribution

It introduces the first resource theory of incompatibility preservability and provides a robustness measure and operational framework for its characterization.

Findings

Defines a robustness measure for incompatibility preservability.

Introduces an entanglement-assisted filter game for characterization.

Provides a framework linking noisy dynamics to the uncertainty principle.

Abstract

The uncertainty principle is one of quantum theory's most foundational features. It underpins a quantum phenomenon called measurement incompatibility -- two physical observables of a single quantum system may not always be measured simultaneously. Apart from being fundamentally important, measurement incompatibility is also a powerful resource in the broad quantum science and technologies, with wide applications to cryptography, communication, random number generation, and device-independent tasks. Since every physical system is unavoidably subject to noise, an important, yet still open, question is how to characterise the ability of noisy quantum dynamics to preserve measurement incompatibility. This work fills this gap by providing the first resource theory of this ability, termed incompatibility preservability. We quantify incompatibility preservability by a robustness measure. Then, we introduce an operational task, entanglement-assisted filter game, to completely characterise both the robustness measure and the conversion of incompatibility preservability. Our results provide a general framework to describe how noisy dynamics affect the uncertainty principle's signature.