Lower bound on the communication cost of simulating bipartite quantum correlations

TL;DR

This paper proves that exactly two bits of communication are necessary to classically simulate quantum correlations from maximally entangled bipartite systems, establishing a lower bound on communication cost.

Contribution

It demonstrates that one bit of communication is insufficient, confirming that two bits are required for perfect simulation of certain quantum correlations.

Findings

One bit of communication cannot simulate maximally entangled four-dimensional systems.

Two bits of communication suffice to reproduce these quantum correlations.

The result establishes a lower bound on classical simulation complexity.

Abstract

Suppose Alice and Bob share a maximally entangled state of any finite dimension and each perform two-outcome measurements on the respective part of the state. It is known, due to the recent result of Regev and Toner, that if a classical model is augmented with two bits of communication then all the quantum correlations arising from these measurements can be reproduced. Here we show that two bits of communication is in fact necessary for the perfect simulation. In particular, we prove that a pair of maximally entangled four-dimensional quantum systems cannot be simulated by a classical model augmented by only one bit of communication.