Hierarchy of Nonlinear Entanglement Dynamics for Continuous Variables

Abstract

The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate high-order Hamiltonians remains unclear. Here, we derive a hierarchy of sufficient and necessary conditions for the positive-partial-transposition separability of bipartite nonlinear quantum states. The proposed criteria detect the nonpositive-partial-transposition inseparability of higher-order moments of states, which provides a systematic framework for the characterization of this kind of entanglement. Through numerical simulation of cubic and quartic Hamiltonians, we demonstrate the existence and competition of a hierarchy of entanglement witnesses, revealing the mechanism underlying such entanglement. Our results may provide a new direction in continuous variable quantum information processing.

arXiv comment6 pages, 2 figures

References in corpus (45)

• Quantum entanglement
• Separability Criterion for Density Matrices
• Quantum information with continuous variables
• Gaussian Quantum Information
• Entanglement detection
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Separability criterion and inseparable mixed states with positive partial transposition
• Quantum computation over continuous variables
• Universal Quantum Computation with Continuous-Variable Cluster States
• The European Quantum Technologies Roadmap
• The Einstein-Podolsky-Rosen paradox: from concepts to applications
• Entangling macroscopic oscillators exploiting radiation pressure
• Bound entangled Gaussian states
• Entanglement conditions for two-mode states
• Inseparability criteria for bipartite quantum states
• Non-Gaussian entanglement distillation for continuous variables
• Teleportation improvement by inconclusive photon subtraction
• Continuous variable quantum teleportation with non-Gaussian resources
• Distillability Criterion for all Bipartite Gaussian States
• Separability Criterion for all bipartite Gaussian States
• The optimal cloning of quantum coherent states is non-Gaussian
• Inseparability inequalities for higher-order moments for bipartite systems
• Observation of Three-Photon Spontaneous Parametric Downconversion in a Superconducting Parametric Cavity
• Detecting multimode entanglement by symplectic uncertainty relations
• Multimode uncertainty relations and separability of continuous variable states
• Entropic Entanglement Criteria for Continuous Variables
• Limitations of quantum computing with Gaussian cluster states
• Criteria for genuine N-partite continuous variable entanglement and Einstein-Podolsky_Rosen steering
• Inseparability criteria based on matrices of moments
• Bound entanglement and continuous variables
• Greatly enhanced intensity-difference squeezing for narrow-band quantum metrology applications
• Uncertainty inequalities as entanglement criteria for negative partial-transpose states
• Continuous variables triple-photon states quantum entanglement
• Comment on ``Inseparability Criteria for Continuous Bipartite Quantum States''
• A Family of Continuous Variable Entanglement Criteria using General Entropy Functions
• Efficient measurement-based quantum computing with continuous-variable systems
• Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements
• Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
• Non-Gaussian Nature and Entanglement of Spontaneous Parametric Nondegenerate Triple-Photon Generation
• Systematic Construction of Genuine Multipartite Entanglement Criteria using Uncertainty Relations
• Non-classicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors II: Criteria based on probabilities
• Criteria to detect genuine multipartite entanglement using spin measurements
• Photonic families of non-Gaussian entangled states and entanglement criteria for continuous-variable systems
• Higher-order EPR correlations and inseparability conditions for continuous variables

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• Gaussian entanglement witness and refined Werner-Wolf criterion for continuous variables
• Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator