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

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.

8 pages

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• Entanglement Thresholds of Doubly-Parametric Quantum Transducers
• Censorship of Quantum Resources in Quantum Networks
• Unbreakable and breakable quantum censorship
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Divergence-free approach for obtaining decompositions of quantum-optical processes
• Entanglement-breaking channels are a quantum memory resource
• Scaling maps of $s$-ordered quasiprobabilities are either nonpositive or completely positive
• Characterizing the Gaussian coherence-breaking channel and its property with assistant entanglement inputs