Device-independent dimension test in a multiparty Bell experiment

TL;DR

This paper introduces a robust, general method for device-independent dimension testing in multiparty Bell experiments, extending previous bipartite approaches and demonstrating advantages in multiparty scenarios.

Contribution

It proposes a new multiparty dimension test based on a prepare-and-distribute scenario, showing tight results and advantages over bipartite tests.

Findings

Test results can be tight in specific examples.

The multiparty test outperforms bipartite-based methods.

Partial state information can reveal additional properties.

Abstract

A device-independent dimension test for a Bell experiment aims to estimate the underlying Hilbert space dimension that is required to produce given measurement statistical data without any other assumptions concerning the quantum apparatus. Previous work mostly deals with the two-party version of this problem. In this paper, we propose a very general and robust approach to test the dimension of any subsystem in a multiparty Bell experiment. Our dimension test stems from the study of a new multiparty scenario which we call prepare-and-distribute. This is like the prepare-and-measure scenario, but the quantum state is sent to multiple, non-communicating parties. Through specific examples, we show that our test results can be tight. Furthermore, we compare the performance of our test to results based on known bipartite tests, and witness remarkable advantage, which indicates that our test is of a true multiparty nature. We conclude by pointing out that with some partial information about the quantum states involved in the experiment, it is possible to learn other interesting properties beyond dimension.