Boson correlations are spurious for classical states

TL;DR

The paper demonstrates that boson correlations in classical states are spurious, arising from statistical ensemble effects and symmetry-breaking, not genuine quantum correlations.

Contribution

It reveals that boson correlations in classical states are due to the Simpson paradox and statistical averaging, challenging the interpretation of nonclassicality.

Findings

Boson correlations in classical states are spurious and due to ensemble averaging.

These correlations are a manifestation of the Simpson paradox caused by symmetry-breaking.

Distinguishing quantum and statistical averages is crucial for understanding nonclassicality.

Abstract

We show that boson correlations from quantum states with a Glauber-Sudarshan representation of their density matrix which provides a well-behaved probability distribution -- including coherent states, thermal states, and all states that can be deemed classical -- are a manifestation of the Simpson paradox: they are spurious correlations from statistical (ensemble) averages over uncorrelated measurements made in varying geometries, due to a process of symmetry-breaking as a confounding factor. Bosonic correlations encoded by the wavefunction appear to be formed in the geometry assumed, which however is not that of the statistical ensemble but varies from realization to realization. This calls to distinguish between quantum and statistical averages and sheds new understandings on the fundamental problems of nonclassicality and quantum advantage.