Tripartite probability distributions and communication complexity

TL;DR

This paper demonstrates that tripartite quantum correlations from Schmidt states can be classically simulated with minimal communication, extending bounds on Bell inequality violations and generalizing to multiple parties.

Contribution

It introduces a method to simulate tripartite quantum correlations with limited classical communication and extends Bell violation bounds to multi-party scenarios.

Findings

Tripartite quantum correlations can be simulated with two bits of communication per direction.

Bell inequality violations are bounded by a factor exponential in the communication bits.

The results generalize to n-party systems with similar bounds.

Abstract

We show that every tripartite quantum correlation generated with a Schmidt state (in particular every correlation generated with the GHZ state) can be simulated with the sending of two bits of classical communication from Alice to Bob and Charlie plus the sending of two bits of classical communication from Bob to Charlie. This extends recent results which showed that the maximal violation of Bell inequalities attainable by these correlations is uniformly bounded. For simplicity, we state and prove the result for three parties, but the generalization to the case of $n$ parties follows easily. We also show that every $n$-partite probability distribution generated with local resources plus $c$-bits of local communication can violate a Bell inequality by at most a factor of $2^c$.