Exact simulation of the GHZ distribution

TL;DR

This paper presents an exact classical simulation protocol for arbitrary measurements on n-partite GHZ states, requiring polynomial communication and randomness, advancing the understanding of simulating quantum correlations.

Contribution

It introduces a novel protocol for simulating multipartite GHZ state measurements with bounded communication and randomness, improving efficiency over previous methods.

Findings

Protocol requires O(n^2) bits of communication for general measurements.

For equatorial measurements, protocol needs only O(n log n) bits of communication.

Simulation can be performed with a constant expected number of rounds.

Abstract

John Bell has shown that the correlations entailed by quantum mechanics cannot be reproduced by a classical process involving non-communicating parties. But can they be simulated with the help of bounded communication? This problem has been studied for more than two decades and it is now well understood in the case of bipartite entanglement. However, the issue was still widely open for multipartite entanglement, even for the simplest case, which is the tripartite Greenberger-Horne-Zeilinger (GHZ) state. We give an exact simulation of arbitrary independent von Neumann measurements on general n-partite GHZ states. Our protocol requires O(n^2) bits of expected communication between the parties, and O(n log n) expected time is sufficient to carry it out in parallel. Furthermore, we need only an expectation of O(n) independent unbiased random bits, with no need for the generation of continuous real random variables nor prior shared random variables. In the case of equatorial measurements, we improve on the prior art with a protocol that needs only O(n log n) bits of communication and O(log^2 n) parallel time. At the cost of a slight increase in the number of bits communicated, these tasks can be accomplished with a constant expected number of rounds.