Macroscopic locality with equal bias reproduces with high fidelity a quantum distribution achieving the Tsirelson's bound

TL;DR

This paper demonstrates that combining Macroscopic Locality with equal bias constraints can closely replicate the quantum distribution at Tsirelson's bound, highlighting differences between ML and Information Causality.

Contribution

It shows that ML with equal bias reproduces the quantum distribution at maximal Bell violation, revealing the non-equivalence of ML and IC.

Findings

ML with equal bias reproduces quantum distribution at Tsirelson's bound

ML and IC are shown to be physically inequivalent principles

The approach highlights the role of additional constraints in quantum correlations

Abstract

Two physical principles, Macroscopic Locality (ML) and Information Causality (IC), so far, have been most successful in distinguishing quantum correlations from post-quantum correlations. However, there are also some post-quantum probability distributions which cannot be distinguished with the help of these principles. Thus, it is interesting to see whether consideration of these two principles, separately, along with some additional physically plausible constraints, can explain some interesting quantum features which are otherwise hard to reproduce. In this paper we show that, in a Bell-CHSH scenario, ML along with constraint of equal-biasness for the concerned observables, almost reproduces the quantum joint probability distribution corresponding to maximal quantum Bell violation, which is unique up to relabeling. From this example and earlier work of Cavalcanti, Salles and Scarani, we conclude that IC and ML are in-equivalent physical principles; satisfying one does not imply that the other is satisfied.