Device-independent tests of classical and quantum dimensions

TL;DR

This paper develops a formal framework for testing the minimum classical or quantum system dimension needed to produce observed measurement data, using dimension witnesses in a black-box scenario.

Contribution

It introduces a general formalism for dimension testing and extends quantum dimension witnesses to arbitrary systems, providing practical examples.

Findings

Derived lower bounds on classical dimensions for given data

Extended quantum dimension witnesses to general quantum systems

Provided simple examples of classical and quantum dimension witnesses

Abstract

We address the problem of testing the dimensionality of classical and quantum systems in a `black-box' scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalise the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.