Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1306.5536 · Physical Review A

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

J. Solomon Ivan, Krishna Kumar Sabapathy, R. Simon

Published Sep 4, 2013• 22 citations
arXivHTMLPDF

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 behavior 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 term ``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.

DOI
10.1103/physreva.88.032302

Related papers

Quantum-optical channels that output only classical states

Krishna Kumar Sabapathy

The Glauber-Sudarshan diagonal ``weight'' function provides a natural divide between the quantum-optical notion of classical and nonclassical states of continuous-variable systems. Based on this demarcation, a channel is said to be nonclassicality breaking if it outputs only classical states for any input state. We focus on multimode bosonic Gaussian channels and classify those that are nonclassicality breaking by introducing a criterion that needs to be satisfied by the matrices representing these channels. The criterion can be interpreted as a nonclassicality benchmark for these channels since it quantifies the threshold noise at which there is a complete nonclassical to classical transition of the output states, i.e., it quantifies the robustness of the nonclassicality of the outputs of the channel against Gaussian noise. We then prove a striking ``duality'' between nonclassicality-breaking and entanglement-breaking bosonic Gaussian channels.

arXiv:1412.5342•Physical Review A•Nov 2, 2015•11 citations

Some aspects of the interplay between bipartite correlations and quantum channels

Krishna Kumar Sabapathy

This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels represent all possible evolutions of states allowed by quantum mechanics while correlations are intrinsic (nonlocal) properties of composite systems. There are four main problems that are addressed (i) the role played by initial system-bath correlations on the subsystem dynamics of an open quantum system, (ii) computation of correlations for two-qubit X-states, (iii) the robustness of non-Gaussian entanglement under symmetric local noisy attenuator and amplifier channels, and finally, (iv) the connection between nonclassicality breaking and entanglement breaking for single-mode bosonic Gaussian channels.

arXiv:1604.08017•Apr 27, 2016•0 citations

Gaussian channels that are eventually entanglement breaking yet asymptotically nonclassicality saving

Sagnik Garai, J. Solomon Ivan

A complete classification of single-mode bosonic Gaussian channels on the basis of being quantum-limited or entanglement breaking under $n$-fold composition is obtained. Parametric forms for all single-mode bosonic Gaussian channels that remain quantum-limited under $n$-fold composition is obtained. It is shown that the obtained parametric forms of quantum-limited amplifier, attenuator, and singular noise channels are entanglement saving, i.e., they do not break entanglement under finite $n$-fold composition. All other single-mode bosonic Gaussian channels, quantum limited or not, are shown to be eventually entanglement breaking. Nonclassicality breaking under multiple composition of a single-mode bosonic Gaussian channel is also studied. We outline a family of single-mode bosonic Gaussian channels that are eventually entanglement breaking, but asymptotically nonclassicality saving. We illustrate examples of channels that are eventually nonclassicality breaking, asymptotically nonclassicality breaking, and asymptotically nonclassicality saving.

Physical Review A•Nov 29, 2018•2 citations

Nonclassicality in phase space and nonclassical correlation

Petr Marek, M. S. Kim, Jinhyoung Lee

Continuous-variable entanglement is a manifestation of nonclassicality of quantum states. In this paper, we attempt to analyze whether and under which conditions nonclassicality can be used as an entanglement criterion. We adopt the well-accepted definition of nonclassicality in the form of lack of well-defined positive Glauber-Sudarshan $P$ function describing the state. After demonstrating that the classicality of subsystems is not sufficient for the nonclassicality of the overall state to be identifiable with entanglement, we focus on Gaussian states and find specific local unitary transformations required to arrive at this equivalency. This is followed by the analysis of quantitative relation between nonclassicality and entanglement.

arXiv:0705.3217•Physical Review A•May 14, 2009•7 citations

Entanglement-breaking channels are a quantum memory resource

Lucas B. Vieira, Huan-Yu Ku, Costantino Budroni

Entanglement-breaking channels (equivalently, measure-and-prepare channels) are quantum operations noted for their ability to destroy multipartite spatial quantum correlations. Inspired by this property, they have also been widely employed in defining notions of “classical memory,” under the assumption that such channels effectively act as a classical resource. In this paper, we show that this assumption is false. By means of multitime correlations, we conclusively show that entanglement-breaking channels are still a quantum resource: A qudit going through an entanglement-breaking channel can generate genuinely nonclassical temporal correlations, i.e., that cannot be simulated by a classical system of same dimension. Our results imply that entanglement-breaking channels cannot generally be employed to characterize classical memory effects without additional assumptions.

arXiv:2402.16789•Physical Review Research•Oct 22, 2025•3 citations

Reassessing the Boundary between Classical and Nonclassical for Individual Quantum Processes

Yujie Zhang, David Schmid, Yìlè Yīng +1 more

There is a received wisdom about where to draw the boundary between classical and nonclassical for various types of quantum processes. For multipartite states, it is the divide between separable and entangled; for channels, the divide between entanglement breaking and not; for sets of measurements, the divide between compatible and incompatible; for assemblages, the divide between unsteerable and steerable. However, these choices have not been motivated by any unified notion of what it means to be classically explainable. One well-motivated notion of classical explainability is the one based on generalized noncontextuality: A set of circuits is classically explainable if a generalized-noncontextual ontological model can realize the statistics they generate. In this work, we show that this notion can be leveraged to define a classical-nonclassical divide for individual quantum processes of arbitrary type. A set of measurements, for example, is judged to be classical if and only if a particular set of circuits—the one obtained by contracting these measurements with every possible quantum state—is classically explainable in the sense just articulated. We begin the task of characterizing where the classical-nonclassical divide lies according to this proposal for a variety of different types of processes. In particular, we show that all of the following are judged to be nonclassical: every entangled state, every set of incompatible measurements, every non-entanglement-breaking channel, and every steerable assemblage. Our proposal differs from the received wisdom, however, insofar as it also judges certain subsets of the complementary classes to be nonclassical, including certain separable states, compatible sets of measurements, entanglement-breaking channels, and unsteerable assemblages. Finally, we prove structure theorems characterizing the classical-nonclassical divide based on whether a process admits of a specific type of frame representation.

arXiv:2503.05884•Physical Review X•Apr 14, 2026•3 citations
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 behavior 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 term ``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.
The Glauber-Sudarshan diagonal ``weight'' function provides a natural divide between the quantum-optical notion of classical and nonclassical states of continuous-variable systems. Based on this demarcation, a channel is said to be nonclassicality breaking if it outputs only classical states for any input state. We focus on multimode bosonic Gaussian channels and classify those that are nonclassicality breaking by introducing a criterion that needs to be satisfied by the matrices representing these channels. The criterion can be interpreted as a nonclassicality benchmark for these channels since it quantifies the threshold noise at which there is a complete nonclassical to classical transition of the output states, i.e., it quantifies the robustness of the nonclassicality of the outputs of the channel against Gaussian noise. We then prove a striking ``duality'' between nonclassicality-breaking and entanglement-breaking bosonic Gaussian channels.
This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels represent all possible evolutions of states allowed by quantum mechanics while correlations are intrinsic (nonlocal) properties of composite systems. There are four main problems that are addressed (i) the role played by initial system-bath correlations on the subsystem dynamics of an open quantum system, (ii) computation of correlations for two-qubit X-states, (iii) the robustness of non-Gaussian entanglement under symmetric local noisy attenuator and amplifier channels, and finally, (iv) the connection between nonclassicality breaking and entanglement breaking for single-mode bosonic Gaussian channels.
A complete classification of single-mode bosonic Gaussian channels on the basis of being quantum-limited or entanglement breaking under nnn-fold composition is obtained. Parametric forms for all single-mode bosonic Gaussian channels that remain quantum-limited under nnn-fold composition is obtained. It is shown that the obtained parametric forms of quantum-limited amplifier, attenuator, and singular noise channels are entanglement saving, i.e., they do not break entanglement under finite nnn-fold composition. All other single-mode bosonic Gaussian channels, quantum limited or not, are shown to be eventually entanglement breaking. Nonclassicality breaking under multiple composition of a single-mode bosonic Gaussian channel is also studied. We outline a family of single-mode bosonic Gaussian channels that are eventually entanglement breaking, but asymptotically nonclassicality saving. We illustrate examples of channels that are eventually nonclassicality breaking, asymptotically nonclassicality breaking, and asymptotically nonclassicality saving.
Continuous-variable entanglement is a manifestation of nonclassicality of quantum states. In this paper, we attempt to analyze whether and under which conditions nonclassicality can be used as an entanglement criterion. We adopt the well-accepted definition of nonclassicality in the form of lack of well-defined positive Glauber-Sudarshan PPP function describing the state. After demonstrating that the classicality of subsystems is not sufficient for the nonclassicality of the overall state to be identifiable with entanglement, we focus on Gaussian states and find specific local unitary transformations required to arrive at this equivalency. This is followed by the analysis of quantitative relation between nonclassicality and entanglement.
Entanglement-breaking channels (equivalently, measure-and-prepare channels) are quantum operations noted for their ability to destroy multipartite spatial quantum correlations. Inspired by this property, they have also been widely employed in defining notions of “classical memory,” under the assumption that such channels effectively act as a classical resource. In this paper, we show that this assumption is false. By means of multitime correlations, we conclusively show that entanglement-breaking channels are still a quantum resource: A qudit going through an entanglement-breaking channel can generate genuinely nonclassical temporal correlations, i.e., that cannot be simulated by a classical system of same dimension. Our results imply that entanglement-breaking channels cannot generally be employed to characterize classical memory effects without additional assumptions.
There is a received wisdom about where to draw the boundary between classical and nonclassical for various types of quantum processes. For multipartite states, it is the divide between separable and entangled; for channels, the divide between entanglement breaking and not; for sets of measurements, the divide between compatible and incompatible; for assemblages, the divide between unsteerable and steerable. However, these choices have not been motivated by any unified notion of what it means to be classically explainable. One well-motivated notion of classical explainability is the one based on generalized noncontextuality: A set of circuits is classically explainable if a generalized-noncontextual ontological model can realize the statistics they generate. In this work, we show that this notion can be leveraged to define a classical-nonclassical divide for individual quantum processes of arbitrary type. A set of measurements, for example, is judged to be classical if and only if a particular set of circuits—the one obtained by contracting these measurements with every possible quantum state—is classically explainable in the sense just articulated. We begin the task of characterizing where the classical-nonclassical divide lies according to this proposal for a variety of different types of processes. In particular, we show that all of the following are judged to be nonclassical: every entangled state, every set of incompatible measurements, every non-entanglement-breaking channel, and every steerable assemblage. Our proposal differs from the received wisdom, however, insofar as it also judges certain subsets of the complementary classes to be nonclassical, including certain separable states, compatible sets of measurements, entanglement-breaking channels, and unsteerable assemblages. Finally, we prove structure theorems characterizing the classical-nonclassical divide based on whether a process admits of a specific type of frame representation.