Mode-Wise Entanglement of Gaussian States

Abstract

We address the decomposition of a multi-mode pure Gaussian state with respect to a bi-partite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and single mode local states at each side. The character of entanglement of the state can therefore be understood modewise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bi-partite entanglement is the sum of the modewise entanglement. This decomposition is generally not applicable to all mixed Gaussian states. However, the result can be extended to a special family of "isotropic" states, characterized by a phase space covariance matrix with a completely degenerate symplectic spectrum.

4 pages, RevTex4. Replaced with revised version with reference added to a previous related paper. Minor typographical errors corrected

References in corpus (8)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Concentrating Partial Entanglement by Local Operations
• Peres-Horodecki separability criterion for continuous variable systems
• Thermodynamics and the Measure of Entanglement
• Entanglement Properties of the Harmonic Chain
• Entanglement purification of Gaussian continuous variable quantum states
• Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States

Cited by in corpus (78)

• Quantum information with continuous variables
• Gaussian Quantum Information
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Quantum optics in the phase space - A tutorial on Gaussian states
• Symplectic invariants, entropic measures and correlations of Gaussian states
• Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Monogamy inequality for distributed Gaussian entanglement
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Unitarily localizable entanglement of Gaussian states
• Detection of vacuum entanglement in a linear ion trap
• Limitations of quantum computing with Gaussian cluster states
• Gaussian entanglement revisited
• Information geometry of Gaussian channels
• Classical algorithm for simulating experimental Gaussian boson sampling
• BCS-like Modewise Entanglement of Fermion Gaussian States
• Gaussian quantum marginal problem
• Gaussian localizable entanglement
• Statistics of multiphoton events in spontaneous parametric down-conversion
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Long-range entanglement in the Dirac vacuum
• Strong no-go theorem for Gaussian quantum bit commitment
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Generic Entanglement and Standard Form for N-mode Pure Gaussian States
• Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
• Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States
• Entanglement of Pure Two-Mode Gaussian States
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Not-so-normal mode decomposition
• Matrix product state algorithms for Gaussian fermionic states
• Minimal energy cost of entanglement extraction
• Holomorphic representation of quantum computations
• Exponentially enhanced quantum communication rate by multiplexing continuous-variable teleportation
• Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state
• Key distillation from Gaussian states by Gaussian operations
• Entanglement structure of quantum fields through local probes
• Spatially Overlapped Partners in Quantum Field Theory
• Non-classical correlations in quantum mechanics and beyond
• Entanglement generation via scattering of two particles with hard-core repulsion
• Hawking Radiation on an Ion Ring in the Quantum Regime
• Computable genuine multimode entanglement measure: Gaussian vs. non-Gaussian
• Entanglement of Solitons in the Frenkel-Kontorova Model
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• Gaussian intrinsic entanglement
• Entanglement Structures in Quantum Field Theories II: Distortions of Vacuum Correlations Through the Lens of Local Observers
• Invariant measures on multimode quantum Gaussian states
• Bosonic and fermionic Gaussian states from Kähler structures
• Preparation of bipartite bound entangled Gaussian states in quantum optics
• Superoscillations underlying remote state preparation for relativistic fields
• Entangled pairs in evaporating black holes without event horizons
• Quantum impurity models using superpositions of fermionic Gaussian states: Practical methods and applications
• On the entanglement of a quantum field with a dispersive medium
• Unified framework to determine Gaussian states in continuous variable systems
• Mixed state localizable entanglement for continuous variables
• Optimal encoding of oscillators into more oscillators
• Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations
• Enhancement of nonclassical properties of two-mode squeezed vacuum state with postselected von Neumann measurement
• Fermionic tensor networks for higher order topological insulators from charge pumping
• A classification of Markovian fermionic Gaussian master equations
• System-bath entanglement of noninteracting fermionic impurities: Equilibrium, transient, and steady-state regimes
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Classical simulation of bosonic linear-optical random circuits beyond linear light cone
• Partial-transpose-guided entanglement classes and minimum noise filtering in many-body Gaussian quantum systems
• Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension
• Gaussian intrinsic entanglement for states with partial minimum uncertainty
• The stellar decomposition of Gaussian quantum states
• Detecting spacelike vacuum entanglement at all distances and promoting negativity to a necessary and sufficient entanglement measure in many-body regimes
• Bipartite and tripartite entanglement in a Bose-Einstein acoustic black hole
• Identification of a natural fieldlike entanglement resource in trapped-ion chains
• Effective thermodynamics of isolated entangled squeezed and coherent states
• Structure of the Phase in Pure Two-Mode Gaussian States
• Interpolated Collision Model Formalism
• Entanglement on curved hypersurfaces: A field-discretizer approach
• Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
• Quantum entanglement of Hawking-Partner modes in expanding cavities
• Finite Gaussian assistance protocols and a conic metric for extremizing spacelike vacuum entanglement
• Vacuum-purified Hawking radiation from evaporating black holes: Lessons from moving mirrors
• A contour for the entanglement negativity of bosonic Gaussian states