A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability

TL;DR

This paper develops a comprehensive resource theory of quantum measurement incompatibility by linking it to quantum programmability, providing a framework for understanding and quantifying this non-classical phenomenon in quantum information tasks.

Contribution

It introduces a novel resource theory of quantum incompatibility based on programmable measurement devices and establishes convertibility conditions using quantum state discrimination.

Findings

Measurement incompatibility is characterized as a quantum resource.

A complete set of convertibility conditions for programmable devices is derived.

The framework connects measurement incompatibility with quantum programmability and state discrimination.

Abstract

Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks such violating a Bell Inequality or nonlocally steering part of an entangled state. In this paper, we characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability. This refers to the temporal freedom a user has in issuing programs to a quantum device. For devices with a classical control and classical output, measurement incompatibility emerges as the essential quantum resource embodied in their functioning. Based on the processing of programmable measurement devices, we construct a quantum resource theory of incompatibility. A complete set of convertibility conditions for programmable devices is derived based on quantum state discrimination with post-measurement information.