Measurement entropy in Generalized Non-Signalling Theory cannot detect bipartite non-locality

TL;DR

This paper characterizes measurement entropy in Generalized Non-Signalling Theory, revealing that it cannot distinguish non-locality since all bipartite entropy vectors are achievable by separable states, unlike quantum entropy.

Contribution

It provides a complete characterization of bipartite measurement entropies in Generalized Non-Signalling Theory, showing non-locality is undetectable through this entropy measure.

Findings

Only subadditivity and non-negativity inequalities hold among entropies.

Any bipartite entropy vector can be realized by separable states.

Measurement entropy cannot detect non-locality in this framework.

Abstract

We consider entropy in Generalized Non-Signalling Theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a bipartite state. We find that the only inequalities amongst these entropies are subadditivity and non-negativity. What is surprising is that non-locality does not play a role - in fact any bipartite entropy vector can be achieved by separable states of the theory. This is in stark contrast to the case of the von Neumann entropy in quantum theory, where only entangled states satisfy S(AB)<S(A).