Nonclassicality breaking is the same as entanglement breaking for bosonic Gaussian channels

Abstract

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