Effective separability of typical entangled many-body states

TL;DR

This paper demonstrates that in large many-body quantum systems, entangled states exhibit correlations indistinguishable from separable mixtures, highlighting an effective classicality emerging in large systems.

Contribution

It shows that typical entangled many-body states behave as separable mixtures in large systems, extending the concept of effective separability beyond specific models.

Findings

Large systems exhibit correlations similar to separable mixtures.

Small bipartite systems' correlations align with large system results.

Effective separability applies broadly to various physical systems.

Abstract

We consider two systems of harmonically trapped particles in a typical pure state of the Hilbert space defined by given values of the particle numbers and energies of the two gases. Such a state is entangled but we show that, for large systems, the resulting correlations between the two gases are identical to those of a separable mixture. This result can be generalized to other physical systems. We discuss the relation of this effective separability to the well-known existence of quantum correlations in any entangled state. We study in detail a small bipartite system and find that its correlations are well explained by the large systems results.