Quantifying non-Gaussianity of quantum-state correlation

Abstract

We consider how to quantify non-Gaussianity for the correlation of a bipartite quantum state by using various measures such as relative entropy and geometric distances. We first show that an intuitive approach, i.e., subtracting the correlation of a reference Gaussian state from that of a target non-Gaussian state, fails to yield a non-negative measure with monotonicity under local Gaussian channels. Our finding clearly manifests that quantum-state correlations generally have no Gaussian extremality. We therefore propose a different approach by introducing relevantly averaged states to address correlation. This enables us to define a non-Gaussianity measure based on, e.g., the trace-distance and the fidelity, fulfilling all requirements as a measure of non-Gaussian correlation. For the case of the fidelity-based measure, we also present readily computable lower bounds of non-Gaussian correlation.

published version, 10 pages, 6 figures

References in corpus (64)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• A computable measure of entanglement
• Introducing Quantum Discord
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• The logarithmic negativity: A full entanglement monotone that is not convex
• Inflation Dynamics and Reheating
• Continuous variable quantum information: Gaussian states and beyond
• On quantum Renyi entropies: a new generalization and some properties
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Continuous-variable teleportation improvement by photon subtraction via conditional measurement
• Gaussian transformations and distillation of entangled Gaussian states
• Extremality of Gaussian quantum states
• Non-Gaussian entanglement distillation for continuous variables
• Proposal for a loophole-free Bell test using homodyne detection
• Teleportation improvement by inconclusive photon subtraction
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Monotonicity of a relative Rényi entropy
• Proposed Test of Quantum Nonlocality for Continuous Variables
• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
• Continuous variable quantum teleportation with non-Gaussian resources
• Quantifying non-Gaussianity for quantum information
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Enhancing quantum entanglement by photon addition and subtraction
• A measure of the non-Gaussian character of a quantum state
• Quantum state engineering by a coherent superposition of photon subtraction and addition
• Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition
• Experimental entanglement distillation of mesoscopic quantum states
• Uhlmann fidelity between two-mode Gaussian states
• Genuine quantum and classical correlations in multipartite systems
• Distillation of the two-mode squeezed state
• Detecting quantum non-Gaussianity via the Wigner function
• Undoing the effect of loss on quantum entanglement
• Preparation of distilled and purified continuous variable entangled states
• Alternative fidelity measure for quantum states
• Experimental test of quantum non-Gaussianity of heralded single photon state
• Experimental distillation of squeezing from non-Gaussian quantum states
• Non-Gaussian Fluctuation and Non-Markovian Effect in the Nuclear Fusion Process: Langevin Dynamics Emerging from Quantum Molecular Dynamics Simulations
• Finite Temperature Critical Behavior of Mutual Information
• Quantum non-Gaussian Depth of Single-Photon States
• Quantum non-Gaussianity witnesses in the phase space
• Entanglement generation and Hamiltonian simulation in Continuous-Variable Systems
• Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments
• Continuous-variable Werner state: separability, nonlocality, squeezing and teleportation
• Second-order superposition operations via Hong-Ou-Mandel interference
• Revealing nonclassicality beyond Gaussian states via a single marginal distribution
• The role of initial entanglement and nonGaussianity in the decoherence of photon number entangled states evolving in a noisy channel
• Testing nonclassicality and non-Gaussianity in phase space
• Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements
• Measures of non-Gaussianity for one-mode field states
• Entanglement distillation for continuous-variables under a thermal environment: Effectiveness of a non-Gaussian operation
• Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction
• Practical purification scheme for decohered coherent-state superpositions via partial homodyne detection
• Linear amplification and quantum cloning for non-Gaussian continuous variables
• Demonstrating multipartite entanglement of single-particle W states: linear optical schemes
• Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to dense coding scheme
• Demonstrating nonclassicality and non-Gaussianity of single-mode fields: Bell-type tests using generalized phase-space distributions
• Simple proof of the robustness of Gaussian entanglement in bosonic noisy channels
• Enhanced multipartite quantum correlations by non-Gaussian operations
• Generating arbitrary photon-number entangled states for continuous-variable quantum informatics
• Convergence of macrostates under reproducible processes
• Comment on "Convergence of macrostates under reproducible processes" [Phys. Lett. A 374: 3715-3717 (2010)]

Cited by in corpus (9)

• Nonclassical Light and Metrological Power: An Introductory Review
• Quantum non-Gaussianity and quantification of nonclassicality
• Enhanced continuous generation of non-Gaussianity through optomechanical modulation
• Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions
• Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states
• Non-Gaussian entanglement swapping
• Phase-space quantum profile of Pöschl-Teller two-level systems
• Detecting Nonclassicality and quantum non-Gaussianity of photon subtracted displaced Fock state
• Complexity of quantum tomography from genuine non-Gaussian entanglement