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

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.

To appear in Phys. Rev. A

References in corpus (5)

• Testing the Hilbert space dimension
• Device-independent tests of classical and quantum dimensions
• A lower bound on the dimension of a quantum system given measured data
• Dimension witnesses and quantum state discrimination
• A new device-independent dimension witness and its experimental implementation

Cited by in corpus (7)

• Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir
• Effects of Hawking radiation on the entropic uncertainty in a Schwarzschild space-time
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Shared randomness and device-independent dimension witnessing
• Communication tasks in operational theories
• A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario
• Device-independent characterizations of a shared quantum state independent of any Bell inequalities