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:1507.03876 · Physical Review A

Gaussian discriminating strength

L. Rigovacca, Alessandro Farace, Antonella De Pasquale, Vittorio Giovannetti

Published Oct 27, 2015• 21 citations
arXivHTMLPDF

Abstract

We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014)]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.

DOI
10.1103/physreva.92.042331

Related papers

Quantifying Discriminating Strength for Gaussian States*

Ruifen Ma, Xiaofei Qi, Jinchuan Hou

Abstract The discriminating strength D S ( ρ AB ) induced by local Gaussian unitary operators for any ( n + m )-mode Gaussian state ρ AB is introduced in [Phys. Rev. A 83 (2011) 042325]. In this paper, we further discuss the quantity by restricting to Hilbert-Schmidt norm. The analytic formulas of D S for two-mode squeezed thermal states and mixed thermal states are given. Then, the relationship between D S ( ρ AB ) and D S ( ( I ⊗ Φ ) ( ρ AB ) ) for some special Gaussian channels Φ is discussed. In addition, D S is compared with Gaussian entanglement for symmetric squeezed thermal states .

Communications in Theoretical Physics•Aug 1, 2018•0 citations

Localizing genuine multimode entanglement: Asymmetric gains via non-Gaussianity

Ratul Banerjee, Saptarshi Roy, Tamoghna Das +1 more

Measurement-based quantum correlation mimics several characteristics of multipartite quantum correlations and at the same time, it reduces the parent system to a smaller subsystem. On the other hand, genuine multipartite entanglement measures can capture certain features of a multisite composite system that are inaccessible via bipartite quantum correlation quantifiers. We merge these two concepts by introducing localizable genuine multimode entanglement for continuous variable systems, both for Gaussian and non-Gaussian multimode parent states. We report a compact form of localizable generalized geometric measure for multimode Gaussian states when Gaussian measurements are performed in some of the modes. We show that non-Gaussian measurements can concentrate more genuine multimode entanglement compared to the Gaussian ones. For non-Gaussian states with non-Gaussian measurements, we find that although four-mode squeezed vacuum state has permutation symmetry with respect to the exchange of first and third modes as well as the second and the fourth modes, the symmetry can be broken by performing measurements in one of the modes in case of addition while for subtraction, such symmetry is preserved, thereby providing a method for distinguishing multimode photon-added and -subtracted states via localizations.

arXiv:2103.10388•Mar 18, 2021•0 citations

Classical-Nonclassical Polarity of Gaussian States

Jiru Liu, Wenchao Ge, Muhammad Suhail Zubairy

Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multimode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the "classical-nonclassical polarity," represented by P. For a single mode, a positive value of P captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multimode systems, a positive P indicates bipartite quantum entanglement. We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multimode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing. Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features.

arXiv:2310.12104•Physical Review Letters•Jun 13, 2024•4 citations

Nonclassicality Invariant of General Two-Mode Gaussian States

Ievgen I. Arkhipov, Jan Peřina, Jiŕí Svozilík +1 more

We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.

arXiv:1601.04868•Scientific Reports•May 23, 2016•38 citations

Quantifying nonclassicality and entanglement of Gaussian states

Xiaoyu Chen

Quantification of nonclassicality and entanglement in a quantum state is crucial for quantum advantage in information processing and computation. Robustness is one of the tractable measures for quantifying quantum resources. Gaussian states are important in continuous variable quantum information for their theoretically simple and experimentally easily accessible. We provide the method of how to calculate the robustness of nonclassicality and enatnglement for Gaussian states. The robustness of nonclassicality or entanglement is demonstrated analytically for one-mode, two-mode Gaussain states and multimode symmetric Gaussian states, the result shows a clear physical meaning for the origin of nonclassicality and entanglement. For squeezed thermal states, the nonclassicality is equal to the entanglement for the two-mode case, while they are far apart for multimode cases.

arXiv:2309.11815•Sep 21, 2023•0 citations

Discriminating strength: a bona fide measure of non-classical correlations

A Farace, Antonella De Pasquale, L Rigovacca +1 more

A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state ρ of a composite system AB as a probe for a quantum illumination task (e.g. see Lloyd 2008 Science 321 1463 ), in which one is asked to remotely discriminate between the two following scenarios: (i) either nothing happens to the probe, or (ii) the subsystem A is transformed via a local unitary whose properties are partially unspecified when producing ρ . This new measure can be seen as the discrete version of the recently introduced interferometric power measure (Girolami et al 2013 e-print arXiv: 1309.1472 ) and, at least for the case in which A is a qubit, it is shown to coincide (up to an irrelevant scaling factor) with the local quantum uncertainty measure of Girolami, Tufarelli and Adesso (2013 Phys. Rev. Lett. 110 240402 ). Analytical expressions are derived which allow us to formally prove that, within the set of separable configurations, the maximum value of our non-classicality measure is achieved over the set of quantum-classical states (i.e. states ρ which admit a statistical unravelling where each element of the associated ensemble is distinguishable via local measures on B ).

arXiv:1402.2870•New Journal of Physics•Jul 4, 2014•39 citations
We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014)]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.
Abstract The discriminating strength D S ( ρ AB ) induced by local Gaussian unitary operators for any ( n + m )-mode Gaussian state ρ AB is introduced in [Phys. Rev. A 83 (2011) 042325]. In this paper, we further discuss the quantity by restricting to Hilbert-Schmidt norm. The analytic formulas of D S for two-mode squeezed thermal states and mixed thermal states are given. Then, the relationship between D S ( ρ AB ) and D S ( ( I ⊗ Φ ) ( ρ AB ) ) for some special Gaussian channels Φ is discussed. In addition, D S is compared with Gaussian entanglement for symmetric squeezed thermal states .
Measurement-based quantum correlation mimics several characteristics of multipartite quantum correlations and at the same time, it reduces the parent system to a smaller subsystem. On the other hand, genuine multipartite entanglement measures can capture certain features of a multisite composite system that are inaccessible via bipartite quantum correlation quantifiers. We merge these two concepts by introducing localizable genuine multimode entanglement for continuous variable systems, both for Gaussian and non-Gaussian multimode parent states. We report a compact form of localizable generalized geometric measure for multimode Gaussian states when Gaussian measurements are performed in some of the modes. We show that non-Gaussian measurements can concentrate more genuine multimode entanglement compared to the Gaussian ones. For non-Gaussian states with non-Gaussian measurements, we find that although four-mode squeezed vacuum state has permutation symmetry with respect to the exchange of first and third modes as well as the second and the fourth modes, the symmetry can be broken by performing measurements in one of the modes in case of addition while for subtraction, such symmetry is preserved, thereby providing a method for distinguishing multimode photon-added and -subtracted states via localizations.
Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multimode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the "classical-nonclassical polarity," represented by P. For a single mode, a positive value of P captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multimode systems, a positive P indicates bipartite quantum entanglement. We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multimode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing. Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features.
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.
Quantification of nonclassicality and entanglement in a quantum state is crucial for quantum advantage in information processing and computation. Robustness is one of the tractable measures for quantifying quantum resources. Gaussian states are important in continuous variable quantum information for their theoretically simple and experimentally easily accessible. We provide the method of how to calculate the robustness of nonclassicality and enatnglement for Gaussian states. The robustness of nonclassicality or entanglement is demonstrated analytically for one-mode, two-mode Gaussain states and multimode symmetric Gaussian states, the result shows a clear physical meaning for the origin of nonclassicality and entanglement. For squeezed thermal states, the nonclassicality is equal to the entanglement for the two-mode case, while they are far apart for multimode cases.
A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state ρ of a composite system AB as a probe for a quantum illumination task (e.g. see Lloyd 2008 Science 321 1463 ), in which one is asked to remotely discriminate between the two following scenarios: (i) either nothing happens to the probe, or (ii) the subsystem A is transformed via a local unitary whose properties are partially unspecified when producing ρ . This new measure can be seen as the discrete version of the recently introduced interferometric power measure (Girolami et al 2013 e-print arXiv: 1309.1472 ) and, at least for the case in which A is a qubit, it is shown to coincide (up to an irrelevant scaling factor) with the local quantum uncertainty measure of Girolami, Tufarelli and Adesso (2013 Phys. Rev. Lett. 110 240402 ). Analytical expressions are derived which allow us to formally prove that, within the set of separable configurations, the maximum value of our non-classicality measure is achieved over the set of quantum-classical states (i.e. states ρ which admit a statistical unravelling where each element of the associated ensemble is distinguishable via local measures on B ).