Bipartite entanglement and the arrow of time

TL;DR

This paper explores the fundamental link between bipartite entanglement and the arrow of time, proposing a new compatibility condition based on local observable algebras and their dynamics.

Contribution

It introduces a necessary and sufficient condition for bipartite entanglement rooted in time orientation compatibility within local observable algebras.

Findings

Identifies a compatibility condition for bipartite entanglement based on time orientations.

Connects entanglement criteria with the thermodynamical notion of time.

Relates the structure of local observable algebras to the arrow of time.

Abstract

We provide a new perspective on the close relationship between entanglement and time. Our main focus is on bipartite entanglement, where this connection is foreshadowed both in the positive partial transpose criterion due to Peres [A. Peres, Phys. Rev. Lett., 77, 1413 (1996)] and in the classification of quantum within more general non-signalling bipartite correlations [M. Frembs and A. D\"oring, arXiv:2204.11471]. Extracting the relevant common features, we identify a necessary and sufficient condition for bipartite entanglement in terms of a compatibility condition with respect to time orientations in local observable algebras, which express the dynamics in the respective subsystems. We discuss the relevance of the latter in the broader context of von Neumann algebras and the thermodynamical notion of time naturally arising within the latter.