Remarks on the tensor product structure of no-signaling theories

TL;DR

This paper investigates the mathematical structure of no-signaling theories within quantum logic, revealing that they form a specific tensor product of single-box logics and are not generalizations of quantum mechanics.

Contribution

It demonstrates that no-signaling box models are a particular tensor product in quantum logic and cannot be viewed as broader than quantum models.

Findings

No-signaling box models are a specific tensor product of single-box logics.

Such tensor product notion is too strong for quantum mechanical logics.

No-signaling models are not generalizations of quantum mechanics.

Abstract

In the quantum logic framework we show that the no-signaling box model is a particular type of tensor product of the logics of single boxes. Such notion of tensor product is too strong to apply in the category of logics of quantum mechanical systems. Consequently, we show that the no-signaling box models cannot be considered as generalizations of quantum mechanical models.