Simulating all non-signalling correlations via classical or quantum theory with negative probabilities

TL;DR

This paper demonstrates that all non-signalling correlations can be simulated using classical or quantum theories by allowing negative probabilities, providing new quasi-classical models for quantum correlations.

Contribution

It introduces a novel approach to simulate non-signalling correlations through relaxing positivity constraints in classical and quantum models.

Findings

Any non-signalling distribution can be generated with negative probabilities.

Two distinct quasi-classical models for quantum correlations are presented.

The models relax positivity constraints on states or measurement functions.

Abstract

Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from classical or quantum theory, by relaxing positivity constraints on either the mixed state shared by the parties, or the local functions which generate measurement outcomes. Our results apply to generic non-signalling correlations, but in particular they yield two distinct quasi-classical models for quantum correlations.