Gaussian transformations and distillation of entangled Gaussian states

Abstract

We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via LOCC Gaussian operations. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [quant-ph/0204052] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.

4 pages, 2 figures, added reference to the related paper by Giedke and Cirac

References in corpus (9)

• Continuous variable quantum cryptography using coherent states
• On the impossibility of distilling Gaussian states with Gaussian operations
• Distillability Criterion for all Bipartite Gaussian States
• Separability Criterion for all bipartite Gaussian States
• Optimal cloning of coherent states with a linear amplifier and beam splitters
• Optical implementation of continuous-variable quantum cloning machines
• Probabilistic implementation of universal quantum processors
• Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
• Conditions for the local manipulation of Gaussian states

Cited by in corpus (263)

• Quantum entanglement
• Quantum information with continuous variables
• Gaussian Quantum Information
• Quantum interface between light and atomic ensembles
• Continuous variable quantum information: Gaussian states and beyond
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Quantum repeaters: From quantum networks to the quantum internet
• Detecting genuine multipartite continuous-variable entanglement
• Positive Wigner functions render classical simulation of quantum computation efficient
• Hybrid quantum information processing
• Entanglement Properties of the Harmonic Chain
• Quantification of Gaussian quantum steering
• Increasing entanglement between Gaussian states by coherent photon subtraction
• A No-Go Theorem for Gaussian Quantum Error Correction
• Non-Gaussian entanglement distillation for continuous variables
• Non-Gaussian Quantum States and Where to Find Them
• Probing multimode squeezing with correlation functions
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states
• Observation of genuine one-way Einstein-Podolsky-Rosen steering
• 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
• Quantifying non-Gaussianity for quantum information
• Driving non-Gaussian to Gaussian states with linear optics
• Convex resource theory of non-Gaussianity
• Gaussian Entanglement of Formation
• The entangling power of passive optical elements
• Enhancing quantum entanglement by photon addition and subtraction
• Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers
• Satellite-Based Continuous-Variable Quantum Communications: State-of-the-Art and a Predictive Outlook
• Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition
• Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
• Optimal entanglement witnesses for continuous-variable systems
• Experimental entanglement distillation of mesoscopic quantum states
• Continuous-Variable Quantum Key Distribution using Thermal States
• Spin squeezing and precision probing with light and samples of atoms in the gaussian approximation
• Measurement-Based Noiseless Linear Amplification for Quantum Communication
• Distillation of the two-mode squeezed state
• Stellar representation of non-Gaussian quantum states
• Gaussian quantum resource theories
• Distillation of continuous-variable entanglement with optical means
• Gaussian systems for quantum enhanced multiple phase estimation
• Non-Gaussianity as a signature of a quantum theory of gravity
• Optimal control of entanglement via quantum feedback
• Limitations of quantum computing with Gaussian cluster states
• Metrological Nonlinear Squeezing Parameter
• Quantum secret sharing with continuous-variable cluster states
• Multi-mode bosonic Gaussian channels
• Operational resource theory of continuous-variable nonclassicality
• Distillation of mixed-state continuous-variable entanglement by photon subtraction
• Experimental demonstration of continuous variable purification of squeezed states
• Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector
• Resource theory of non-Gaussian operations
• Probing the negative Wigner function of a pulsed single photon point by point
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox
• Experimental distillation of squeezing from non-Gaussian quantum states
• Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology
• Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light
• Nonclassical Light and Metrological Power: An Introductory Review
• Two-way quantum cryptography at different wavelengths
• Strategies for enhancing quantum entanglement by local photon subtraction
• A compact entanglement distillery
• Entanglement generation and Hamiltonian simulation in Continuous-Variable Systems
• Gaussian entanglement revisited
• Repeaters for Continuous Variable Quantum Communication
• Enhancing quantum entanglement and quantum teleportation for two-mode squeezed vacuum state by local quantum-optical catalysis
• Terahertz Quantum Cryptography
• Bell's inequality for conditional probabilities as a test for quantum-like behaviour of mind
• Estimation of a classical parameter with gaussian probes: magnetometry with collective atomic spins
• Entanglement and nonclassicality of photon-added two-mode squeezed thermal state
• Loophole-free test of quantum non-locality using high-efficiency homodyne detectors
• Markovian feedback to control continuous variable entanglement
• Reliable source of conditional non-Gaussian states from single-mode thermal fields
• Entanglement concentration of continuous variable quantum states
• Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
• Local Gaussian operations can enhance continuous-variable entanglement distillation
• Experimental realization of a dynamic squeezing gate
• Gaussian quantum marginal problem
• Enhanced noise resilience of the surface-GKP code via designed bias
• Distillation and purification of symmetric entangled Gaussian states
• Revealing nonclassicality beyond Gaussian states via a single marginal distribution
• Capacity of optical communication in loss and noise with general Gaussian receivers
• The role of initial entanglement and nonGaussianity in the decoherence of photon number entangled states evolving in a noisy channel
• Modular network for high-rate quantum conferencing
• Improving entanglement concentration of Gaussian states by local displacements
• Testing nonclassicality and non-Gaussianity in phase space
• Distinguishing two single-mode Gaussian states by homodyne detection: An information-theoretic approach
• Continuous variable entanglement distillation of Non-Gaussian Mixed States
• Witnessing Wigner Negativity
• Efficient representation of Gaussian states for multi-mode non-Gaussian quantum state engineering via subtraction of arbitrary number of photons
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Efficient measurement-based quantum computing with continuous-variable systems
• Conditional measurements on multimode pairwise entangled states from spontaneous parametric downconversion
• Experimental test of strongly non-classical character of a noisy squeezed single-photon state
• Gaussian error correction of quantum states in a correlated noisy channel
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Could Gaussian regenerative stations act as quantum repeaters?
• Quantum non-Gaussianity and secure quantum communication
• Entanglement distillation for continuous-variables under a thermal environment: Effectiveness of a non-Gaussian operation
• Experimental purification of coherent states
• Complete elimination of information leakage in continuous-variable quantum communication channels
• The optimal unitary dilation for bosonic Gaussian channels
• Characterizing photon number statistics using conjugate optical homodyne detection
• Continuous variable methods in relativistic quantum information: Characterisation of quantum and classical correlations of scalar field modes in noninertial frames
• Gaussian Entanglement for Quantum Key Distribution from a Single-Mode Squeezing Source
• Continuous-variable entanglement distillation and non-commutative central limit theorems
• Photon-by-photon quantum light state engineering
• Time-evolution of nonlinear optomechanical systems: Interplay of mechanical squeezing and non-Gaussianity
• Dynamics-Based Entanglement Witnesses for Non-Gaussian States of Harmonic Oscillators
• Direct probing of the Wigner function by time-multiplexed detection of photon statistics
• Improving continuous-variable entanglement distribution by separable states
• Non-Gaussian states produced by close-to-threshold optical parametric oscillators: role of classical and quantum fluctuations
• Magnetometry with entangled atomic samples
• Quantifying non-Gaussianity of quantum-state correlation
• Matrix product state algorithms for Gaussian fermionic states
• Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator
• Gaussification and entanglement distillation of continuous variable systems: a unifying picture
• Environmental Assisted Quantum Information Correction for Continuous Variables
• Theory of genuine tripartite nonlocality of Gaussian states
• Multi-step two-copy distillation of squeezed states via two photon subtraction
• Detection of non-Gaussian entangled states with an improved continuous-variable separability criterion
• Holomorphic representation of quantum computations
• Squeezer-based pulsed optomechanical interface
• On the P-representable subset of all bipartite Gaussian separable states
• 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
• From log-determinant inequalities to Gaussian entanglement via recoverability theory
• Simple proof of the robustness of Gaussian entanglement in bosonic noisy channels
• Enhanced continuous generation of non-Gaussianity through optomechanical modulation
• Manipulation of collective quantum states in Bose-Einstein condensates by continuous imaging
• Key distillation from Gaussian states by Gaussian operations
• Non-classical correlations in quantum mechanics and beyond
• Continuous-variable entanglement distillation by cascaded photon replacement
• Characterizing Multipartite Non-Gaussian Entanglement for Three-Mode Spontaneous Parametric Down-Conversion Process
• Enhanced multipartite quantum correlations by non-Gaussian operations
• Entanglement properties of optical coherent states under amplitude damping
• All phase-space linear bosonic channels are approximately Gaussian dilatable
• Violations of Bell's inequality for Gaussian states with homodyne detection and nonlinear interactions
• Continuous-variable quantum communication
• Generation of quantum states with nonlinear squeezing by Kerr nonlinearity
• Bosonic quantum communication across arbitrarily high loss channels
• Quantum non-Gaussianity of frequency up-converted single photons
• Channel purification via continuous-variable quantum teleportation with Gaussian post-selection
• Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems
• Magic Resource Can Enhance the Quantum Capacity of Channels
• Quantifying the nonlinearity of a quantum oscillator
• Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions
• Non-Markovianity Hierarchy of Gaussian Processes and Quantum Amplification
• Characterization and quantification of symmetric Gaussian state entanglement through a local classicality criterion
• Operational Quantification of Continuous Variable Correlations
• Correlation-pattern-based Continuous-variable Entanglement Detection through Neural Networks
• Faithful measure of Quantum non-Gaussianity via quantum relative entropy
• Entanglement quantification from incomplete measurements: Applications using photon-number-resolving weak homodyne detectors
• Gaussian benchmark for optical communication aiming towards ultimate capacity
• Assisted concentration of Gaussian resources
• Theoretical Analysis of an Ideal Noiseless Linear Amplifier for Einstein-Podolsky-Rosen Entanglement Distillation
• Rapid cooling of a strain-coupled oscillator by optical phaseshift measurement
• Entanglement Enhanced Estimation of a Parameter Embedded in Multiple Phases
• Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states
• Gaussian State Description of Squeezed Light
• Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States
• Generation of picosecond pulsed coherent state superpositions
• Subtraction and Addition of Propagating Photons by Two-Level Emitters
• Entanglement convertibility for infinite dimensional pure bipartite states
• Displacement-enhanced entanglement distillation of single-mode-squeezed entangled states
• Displacement-enhanced continuous-variable entanglement concentration
• Conditional preparation of arbitrary atomic Dicke states
• Boosting the generation rate of squeezed single-photon states by generalized photon subtraction
• Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator
• Analyzing the Gaussian character of the spectral quantum state of light via quantum noise measurements
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Verifying single-mode nonclassicality beyond negativity in phase space
• Gaussian intrinsic entanglement
• No-activation theorem for Gaussian nonclassical correlations by Gaussian operations
• Quantum Hypergraph States in Continuous Variables
• Photon subtraction from traveling fields - recent experimental demonstrations
• Entanglement in Gaussian matrix-product states
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Quantum state engineering, purification, and number resolved photon detection with high finesse optical cavities
• Non-Gaussianity of multiple photon subtracted thermal states in terms of compound-Poisson photon number distribution parameters: theory and experiment
• Manipulation of single-photon states encoded in transverse spatial modes: possible and impossible tasks
• Interconversion of pure Gaussian states using non-Gaussian operations
• On the experimental feasibility of continuous-variable optical entanglement distillation
• Certification of non-Gaussian Einstein-Podolsky-Rosen Steering
• Enabling entanglement distillation via optomechanics
• Realignment Entanglement Criterion for Continuous Bipartite Symmetric Quantum States
• Conversion of Gaussian states under incoherent Gaussian operations
• Optimal entanglement enhancing via conditional measurements
• Extended analysis of distillation and purification of squeezed states of light
• Multiple copy distillation and purification of phase diffused squeezed states
• Entanglement engineering of optomechanical systems by reinforcement learning
• Efficient detection of nonclassicality using moments of the Wigner function
• Secret key rate of a continuous-variable quantum-key-distribution scheme when the detection process is inaccessible to eavesdroppers
• Entanglement in the Bogoliubov vacuum
• Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state
• Quantum error correction and detection: quantitative analysis of a coherent-state amplitude damping code
• The role of the non-Gaussianity plays in the enhancement of the fidelity in continuous variable quantum teleportation
• Genuine tripartite entanglement and nonlocality in Bose-Einstein condensates by collective atomic recoil
• Maximum entanglement of formation for a two-mode Gaussian state over passive operations
• Non-Gaussian state generation certified using the EPR-steering inequality
• Heralded processes on continuous-variable spaces as quantum maps
• Nonclassical states of levitated macroscopic objects beyond the ground state
• Gaussian intrinsic entanglement: An entanglement quantifier based on secret correlations
• Photon number discrimination without a photon counter and its application to reconstructing non-Gaussian states
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Gaussian Operations and Privacy
• Cross talk compensation in multimode continuous-variable entanglement distribution
• Engineering continuous and discrete variable quantum vortex states by nonlocal photon subtraction in a reconfigurable photonic chip
• Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel
• A compact entanglement distillery using realistic quantum memories
• Single phase and correlated phase estimation with multi-photon annihilated squeezed vacuum states: An energy balancing scenario
• Entanglement concentration with different measurement in a 3-mode optomechanical system
• Optical implementation and entanglement distribution in Gaussian valence bond states
• Advantage of probabilistic non-Gaussian operations in the distillation of single mode squeezed vacuum state
• Detecting Nonclassicality and quantum non-Gaussianity of photon subtracted displaced Fock state
• Realignment separability criterion assisted with filtration for detecting continuous-variable entanglement
• Amplification uncertainty relation for probabilistic amplifiers
• Minkowski structure for purity and entanglement of Gaussian bipartite states
• Graphical Framework for Non-Gaussian Quantum States
• Resource distillation in convex Gaussian resource theories
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations
• Minimization of information leakage in continuous-variable quantum key distribution
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Entanglement Enhancement in Multimode Integrated Circuits
• Impossibility of bosonic autonomous entanglement engines in the weak-coupling limit
• Transformations of symmetric multipartite Gaussian states by Gaussian LOCC
• Temporal Quantum Noise Reduction Acquired by an Electron-Multiplying Charge-Coupled-Device Camera
• Steady-state tripartite non-Gaussian entanglement and steering in output field from intracavity triple-photon parametric downconversion
• The stellar decomposition of Gaussian quantum states
• Entanglement-based quantum key distribution with non-Gaussian continuous variables
• Optimal squeezing and entanglement from noisy Gaussian operations
• Building trust for continuous variable quantum states
• Improving Continuous-variable Quantum Channels with Unitary Averaging
• Quantum Information with Continuous Variable systems
• Complexity of quantum tomography from genuine non-Gaussian entanglement
• Analyzing the free states of one quantum resource theory as resource states of another
• Physical properties of the Schur complement of local covariance matrices
• Local entanglement of multidimensional continuous-variable systems
• Non-Gaussian macroscopic entanglement of motion in a hybrid electromechanical device
• Entanglement distribution maximization over one-side Gaussian noisy channel
• Gaussian work extraction from random Gaussian states is nearly impossible
• Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
• No real advantage of photon subtraction and displacement in continuous variable measurement device independent quantum key distribution
• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources
• Nonlinear squeezing of superpositions of quadrature eigenstates
• Experimental investigation of heralded Gaussification of phase-randomized coherent states of light
• Analyzing performance of $f$-deformed displaced Fock state in continuous-variable quantum teleportation
• Detecting nonclassicality and non-Gaussianity of a coherent superposed quantum state
• Simplified scheme for continuous-variable entanglement distillation: multicopy distillation of Gaussian entanglement without heralding Gaussian measurements
• Sub-Bath Cooling in Bosonic Systems: Gaussian Constraints and Non-Gaussian Enhancements
• Tabletop reversibility of phase-covariant operations
• Detecting strongly non-Gaussian entanglement
• Sharing classical secrets with continuous-variable entanglement: Composable security and network coding advantage
• Teleportation improvement by non-deterministic noiseless linear amplification
• Generation and Manipulation of Entanglement in Quantum Optical Systems
• The Interplay between Quantum Contextuality and Wigner Negativity
• Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problem
• Majorization theoretical approach to entanglement enhancement via local filtration
• Continuous Generation and Stabilization of Mesoscopic Field Superposition States in a Quantum Circuit
• Finite Gaussian assistance protocols and a conic metric for extremizing spacelike vacuum entanglement
• Optomagnonic continuous-variable quantum teleportation enhanced by non-Gaussian distillation
• The symplectic rank of non-Gaussian quantum states