From no-signalling to quantum states

TL;DR

This paper explores the foundational principles distinguishing quantum states from broader non-signalling correlations, proposing a no-disturbance extension that characterizes quantum states via joint probability distributions.

Contribution

It introduces a no-disturbance extension of no-signalling and proves its correspondence with bipartite quantum states considering time orientation.

Findings

No-disturbance extension characterizes quantum states

Bipartite quantum states linked to non-signalling distributions with no-disturbance

Time orientation plays a role in the quantum state correspondence

Abstract

Characterising quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It has been shown that when considered with respect to so-called locally quantum observables, bipartite non-signalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) non-signalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalisation of no-signalling in the form of no-disturbance to dilated systems. We prove that non-signalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.