Testing the Hilbert space dimension

TL;DR

This paper introduces the concept of dimension witnesses to determine the minimal Hilbert space dimension needed to produce given quantum correlations, advancing the understanding of quantum system complexity.

Contribution

It proposes a new method to lower-bound the Hilbert space dimension from measurement correlations, pioneering a foundational approach in quantum information theory.

Findings

Dimension witnesses can effectively bound the minimal Hilbert space dimension.

The approach provides a new tool for characterizing quantum systems.

This work opens pathways for further research in quantum dimension certification.

Abstract

Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describes such correlations? We introduce the concept of dimension witness to put lower bounds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and Quantum Information applications.