Bipartite quantum states admitting a causal explanation

TL;DR

This paper establishes a link between bipartite quantum states and their causal explanations, showing that separable states are compatible with direct causal influence and providing criteria for temporal compatibility.

Contribution

It proves that all bipartite separable states are temporally compatible with direct causal influence and introduces operational and mathematical criteria for temporal compatibility.

Findings

Separable states are compatible with direct causal influence.

Entangled states are not compatible with direct causal influence.

Provides necessary and sufficient conditions for temporal compatibility.

Abstract

The statistics of local measurements of joint quantum systems can sometimes be used to distinguish the spatiotemporal structure in which they were measured. We first prove that every bipartite separable density matrix is temporally compatible with direct causal influence for arbitrary finite-dimensional quantum systems and measurements of a tomographically-complete class of observables, which includes all Pauli observables in the case of multi-qubit systems. Equivalently, if a bipartite density matrix is not temporally compatible with direct causal influence, then it must be entangled. We also provide an operational meaning for the two temporal evolutions consistent with such correlations in terms of generalized dephasing channels and pretty good measurements. The two temporal evolutions are Bayesian inverses of each other, which is different from them being Petz recovery maps of each other. Finally, we prove necessary and sufficient conditions for an arbitrary bipartite quantum state to be temporally compatible, thereby providing a temporal analogue of the positive partial transpose criterion valid for quantum systems of any dimension.