The signaling dimension of physical systems

TL;DR

This paper reviews the concept of signaling dimension in physical systems, highlighting its significance in understanding the classical simulation of quantum correlations and discussing key results like the equivalence to Hilbert space dimension.

Contribution

It provides a comprehensive overview of signaling dimension, emphasizing its foundational role and recent advances in quantum systems.

Findings

Signaling dimension of quantum systems equals their Hilbert space dimension.

Reviewed key results and their implications for classical simulation of quantum correlations.

Highlighted the importance of signaling dimension in quantum information theory.

Abstract

The signaling dimension of a physical system is the minimum dimension of a classical channel that can reproduce the set of input-output correlations attainable by the given system. Here we put the signaling dimension into perspective by reviewing some of the main known results on the topic, starting from Frenkel and Weiner's 2015 breakthrough showing that the signaling dimension of any quantum system is equal to its Hilbert space dimension.