Quantum incompatibility in collective measurements

TL;DR

This paper explores quantum measurement compatibility when multiple copies of a system are available, introducing new measures and structures to understand joint measurability in this multi-copy context.

Contribution

It introduces the index of incompatibility and the compatibility stack, providing a structural theorem for multi-copy joint observables and their realizations.

Findings

All abstract compatibility stacks with three vertices can be realized quantum mechanically.

The index of incompatibility quantifies multi-copy measurement incompatibility.

A general structure theorem for multi-copy joint observables is established.

Abstract

We study the compatibility (or joint measurability) of quantum observables in a setting where the experimenter has access to multiple copies of a given quantum system, rather than performing the experiments on each individual copy separately. We introduce the index of incompatibility as a quantifier of incompatibility in this multi-copy setting, as well as the notion of compatibility stack representing the various compatibility relations present in a given set of observables. We then prove a general structure theorem for multi-copy joint observables, and use it to prove that all abstract compatibility stacks with three vertices have realizations in terms of quantum observables.