Non-signalling theories and generalized probability

TL;DR

This paper rigorously justifies the use of probability in non-signalling theories, proving their correctness, revealing new properties, and providing tools for analyzing complex systems.

Contribution

It offers a rigorous mathematical foundation for non-signalling theories, confirming their validity and extending their analysis to more complex systems.

Findings

Proof of correctness of non-signalling models

Discovery of new properties of non-signalling boxes

Development of new analytical tools for complex systems

Abstract

We provide mathematicaly rigorous justification of using term "probability" in connection to the so called non-signalling theories,known also as Popescu's and Rohrlich's box worlds. No only do we prove correctness of these models (in the sense that they describe composite system of two independent subsystems) but we obtain new properties of non-signalling boxes and expose new tools for further investigation. Moreover, it allows strightforward generalization to more complicated systems.