An Invitation to Quantum Incompatibility

TL;DR

This paper provides an overview of quantum incompatibility, a fundamental concept explaining various impossibility results in quantum theory like no-cloning and no information without disturbance.

Contribution

It offers a concise overview of quantum incompatibility, highlighting its role in understanding key impossibility statements in quantum physics.

Findings

Quantum incompatibility underpins key quantum impossibility results

Incompatibility links to no-cloning and disturbance in quantum systems

Provides a unified perspective on quantum limitations

Abstract

In the context of a physical theory, two devices, A and B, described by the theory are called incompatible if the theory does not allow the existence of a third device C that would have both A and B as its components. Incompatibility is a fascinating aspect of physical theories, especially in the case of quantum theory. The concept of incompatibility gives a common ground for several famous impossibility statements within quantum theory, such as ``no-cloning'' and ``no information without disturbance''; these can be all seen as statements about incompatibility of certain devices. The purpose of this paper is to give a concise overview of some of the central aspects of incompatibility.