Discord and non-classicality in probabilistic theories

TL;DR

This paper extends the concept of quantum discord to general probabilistic theories, demonstrating that non-null discord signifies non-classicality beyond quantum mechanics, with classical theory being the only one where all states have zero discord.

Contribution

It introduces a generalized discord measure for probabilistic theories and proves that only classical probability theory has zero discord for all states.

Findings

All states in classical probability theory have null discord.

Non-null discord indicates non-classicality in probabilistic theories.

Discord serves as a signature of non-classicality beyond quantum mechanics.

Abstract

Quantum discord quantifies non-classical correlations in quantum states. We introduce discord for states in causal probabilistic theories, inspired by the original definition proposed in Ref. [17]. We show that the only probabilistic theory in which all states have null discord is classical probability theory. Non-null discord is then not just a quantum feature, but a generic signature of non-classicality.