Entanglement and superposition are equivalent concepts in any physical theory

TL;DR

This paper proves that in any physical theory, the concepts of entanglement and superposition are fundamentally equivalent, establishing a universal link between non-classicality, entanglement, and superposition principles across all probabilistic theories.

Contribution

It demonstrates that entanglement and superposition are equivalent in all non-classical theories, providing a theory-independent foundation for their relationship.

Findings

All non-classical GPTs exhibit state-measurement incompatibility.

A version of the BB84 protocol is constructed for any non-classical GPT.

Entanglement and superposition are universally equivalent in non-classical theories.

Abstract

We prove that any two general probabilistic theories (GPTs) are entangleable, in the sense that their composite exhibits either entangled states or entangled measurements, if and only if they are both non-classical, meaning that neither of the state spaces is a simplex. This establishes the universal equivalence of the (local) superposition principle and the existence of global entanglement, valid in a fully theory-independent way. As an application of our techniques, we show that all non-classical GPTs exhibit a strong form of incompatibility of states and measurements, and use this to construct a version of the BB84 protocol that works in any non-classical GPT.