Strongly Incompatible Quantum Devices

TL;DR

This paper broadens the concept of measurement compatibility in quantum mechanics, introducing and characterizing notions of incompatibility and strong incompatibility among quantum devices.

Contribution

It extends the idea of joint measurability to all measurement devices and rigorously defines and distinguishes between incompatibility and strong incompatibility.

Findings

Incompatibility and strong incompatibility are formally characterized.

Examples demonstrate the difference between incompatibility and strong incompatibility.

The work generalizes the concept of measurement incompatibility beyond traditional observables.

Abstract

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.