Bounding the quantum dimension with contextuality

TL;DR

This paper demonstrates how quantum contextuality can be used to certify lower bounds on the dimension of quantum systems via dimension witnesses, which are robust and applicable regardless of the quantum state.

Contribution

It introduces dimension witnesses based on noncontextuality inequalities that are state-independent and robust against noise, providing a new method for certifying quantum system dimensions.

Findings

Dimension witnesses can certify lower bounds on quantum system dimensions.

The proposed witnesses are robust against noise and imperfections.

A recent experiment effectively implemented a state-independent quantum dimension witness.

Abstract

We show that the phenomenon of quantum contextuality can be used to certify lower bounds on the dimension accessed by the measurement devices. To prove this, we derive bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. The resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness.