Popescu-Rohrlich box implementation in general probabilistic theory of processes

TL;DR

This paper demonstrates the existence of Popescu-Rohrlich nonlocal boxes within classical and quantum frameworks, providing explicit constructions and a non-quantum resource-based implementation, advancing understanding of nonlocal correlations.

Contribution

It introduces an explicit measure-and-prepare channel realizing Popescu-Rohrlich boxes in generalized probabilistic processes, and presents a non-quantum, post-selection-based implementation.

Findings

Popescu-Rohrlich boxes exist in classical and quantum theories.

Explicit measure-and-prepare channel realization provided.

Non-quantum resource-based implementation demonstrated.

Abstract

It is shown that Popescu-Rohrlich nonlocal boxes (beating the Tsirelson bound for Bell inequality) do exist in the existing structures of both quantum and classical theory. In particular, we design an explicit example of measure-and-prepare nonlocal (but no-signaling) channel being the realization of nonlocal and no-signaling Popescu-Rohrlich box within the generalized probabilistic theory of processes. Further we present a post-selection-based spatially non-local implementation and show it does not require truly quantum resources, hence, improving the previously known results. Interpretation and potential (spatially non-local) simulation of this form of process nonlocality and the protocol is discussed.