Joint system quantum descriptions arising from local quantumness

TL;DR

This paper shows that bipartite correlations from non-signalling systems with local quantum descriptions are limited by quantum bounds even when dropping finite-dimensionality, if measurements commute rather than tensor product.

Contribution

It extends the understanding of quantum correlations to infinite-dimensional systems under commutativity assumptions, challenging the necessity of tensor product structures.

Findings

Quantum bounds hold under commutativity without finite-dimensionality.

Tensor product structure may not be necessary for quantum correlation limits.

Results suggest new perspectives on the foundations of quantum theory.

Abstract

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely.