Is nonclassicality-breaking the same thing as entanglement-breaking?

TL;DR

This paper demonstrates that, for bosonic Gaussian channels, nonclassicality-breaking channels are essentially equivalent to entanglement-breaking channels, clarifying the relationship between nonclassicality and entanglement in quantum systems.

Contribution

It establishes the equivalence of nonclassicality-breaking and entanglement-breaking channels for bosonic Gaussian channels, advancing understanding of their relationship without bipartite system reference.

Findings

Nonclassicality-breaking channels are equivalent to entanglement-breaking channels in bosonic Gaussian channels.

The analysis classifies channels into nonclassicality-based and entanglement-based types.

The result deepens the intuitive link between nonclassicality and entanglement.

Abstract

Nonclassicality and entanglement are notions fundamental to quantum information processes involving continuous variable systems. That these two notions are intimately related has been intuitively appreciated for quite some time. An aspect of considerable interest is the behaviour of these attributes of a state under the action of a noisy channel. Inspired by the notion of entanglement-breaking channels, we define the concept of nonclassicality-breaking channels in a natural manner. We show that the notion of nonclassicality-breaking is essentially equivalent---in a clearly defined sense of the phrase `essentially'---to the notion of entanglement-breaking, as far as bosonic Gaussian channels are concerned. This is notwithstanding the fact that the very notion of entanglement-breaking requires reference to a bipartite system, whereas the definition of nonclassicality-breaking makes no such reference. Our analysis rests on our classification of channels into nonclassicality-based, as against entanglement-based, types of canonical forms. Our result takes ones intuitive understanding of the close relationship between nonclassicality and entanglement a step closer.