Device-independent dimension tests in the prepare-and-measure scenario

TL;DR

This paper develops a method to estimate the dimension of unknown quantum systems in a device-independent way using measurement data, providing new insights into quantum dimension witnesses and the structure of quantum correlations.

Contribution

It introduces a lower bound on quantum system dimension based solely on measurement statistics in the prepare-and-measure scenario, advancing understanding of quantum dimension witnesses.

Findings

The bound performs well on various examples.

Provides new insights into the concept of dimension witness.

Shows that restricted-dimensional correlations are not always convex.

Abstract

Analyzing the dimension of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. In this paper, we consider this problem in the prepare-and-measure scenario. Specifically, we provide a lower bound on the dimension of the prepared quantum systems which is a function that only depends on the measurement statistics. Furthermore, we show that our bound performs well on several examples. {In particular}, we show that our bound provides new insights into the notion of dimension witness, and we also use it to show that the sets of restricted-dimensional prepare-and-measure correlations are not always convex.