Criteria for genuine N-partite continuous variable entanglement and Einstein-Podolsky_Rosen steering

Abstract

Following previous work, we distinguish between genuine $N$-partite entanglement and full $N$-partite inseparability. Accordingly, we derive criteria to detect genuine multipartite entanglement using continuous variable (position and momentum) measurements. Our criteria are similar but different to those based on the van Loock-Furusawa inequalities, which detect full $N$-partite inseparability. We explain how the criteria can be used to detect the genuine $N$-partite entanglement of continuous variable states generated from squeezed and vacuum state inputs, including the continuous variable Greenberger-Horne-Zeilinger state, with explicit predictions for up to $N=9$. This makes our work accessible to experiment. For $N=3$, we also present criteria for tripartite Einstein-Podolsky-Rosen (EPR) steering. These criteria provide a means to demonstrate a genuine three-party EPR paradox, in which any single party is steerable by the remaining two parties.

19 pages, 14 Figures, many new proofs and results added

References in corpus (19)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• 14-qubit entanglement: creation and coherence
• Nonlinear atom interferometer surpasses classical precision limit
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Experimental entanglement of six photons in graph states
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Robust entanglement of a micromechanical resonator with output optical fields
• Taming multiparticle entanglement
• Experimental entanglement of a six-photon symmetric Dicke state
• Deterministic quantum teleportation of photonic quantum bits by a hybrid technique
• Experimental demonstration of three-color entanglement
• Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator
• Monogamy inequalities for the EPR paradox and quantum steering
• Experimental violation of Svetlichny's inequality
• Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics
• Detecting faked continuous variable entanglement using one-sided device-independent entanglement witnesses
• Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

Cited by in corpus (52)

• Modes and states in Quantum Optics
• Spatially distributed multipartite entanglement enables Einstein-Podolsky-Rosen steering of atomic clouds
• Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
• Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism
• Generating Multimode Entangled Microwaves with a Superconducting Parametric Cavity
• Tripartite Genuine Non-Gaussian Entanglement in Three-Mode Spontaneous Parametric Downconversion
• Continuous variables triple-photon states quantum entanglement
• Delayed sudden death of entanglement at exceptional points
• Probing quantum correlations in many-body systems: a review of scalable methods
• Tripartite entanglement: Foundations and applications
• Simulating complex networks in phase space: Gaussian boson sampling
• Influence of pump coherence on the quantum properties of spontaneous parametric down-conversion
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
• Systematic Construction of Genuine Multipartite Entanglement Criteria using Uncertainty Relations
• Entanglement and squeezing in continuous-variable systems
• Relating spin squeezing to multipartite entanglement criteria for particles and modes
• Quantum correlations across two octaves from combined up and down conversion
• Multipartite entanglement in a microwave frequency comb
• Experimental generation of tripartite polarization entangled states of bright optical beams
• Characterizing Multipartite Non-Gaussian Entanglement for Three-Mode Spontaneous Parametric Down-Conversion Process
• Hierarchy of Nonlinear Entanglement Dynamics for Continuous Variables
• Generalized conditions for genuine multipartite continuous-variable entanglement
• Tripartite correlations over two octaves from cascaded harmonic generation
• Switchable bipartite and genuine tripartite entanglement via an optoelectromechanical interface
• Criteria to detect genuine multipartite entanglement using spin measurements
• Generation and structuring of multipartite entanglement in Josephson parametric system
• Zero supermode-based multipartite entanglement in ${\chi }^{(2)}$ nonlinear waveguides arrays
• Simulating macroscopic quantum correlations in linear networks
• Certification of non-Gaussian Einstein-Podolsky-Rosen Steering
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Tripartite and bipartite entanglement in continuous-variable tripartite systems
• Genuine multipartite nonlocality of permutationally invariant Gaussian states
• Genuine tripartite entanglement in graviton-matter interactions
• Entanglement via a three-well Bose-Hubbard system and via an optical beamsplitter
• Quantum behaviour of open pumped and damped Bose-Hubbard trimers
• Multi-copy activation of genuine multipartite entanglement in continuous-variable systems
• Entanglement of Local Hidden States
• Quantifying Tripartite Spatial and Energy-Time Entanglement in Nonlinear Optics
• Minimal criteria for continuous-variable genuine multipartite entanglement
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Robustness of entanglement in a non-Hermitian cavity-optomechanical system even away from exceptional points
• Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator
• Quantum behaviour of pumped and damped triangular Bose Hubbard systems
• Information back-flow in quantum non-Markovian dynamics and its connection to teleportation
• The versatility of continuous-variable asymmetric tripartite entanglement allows Alice and Clare to keep secrets from Bob
• Witnessing genuine multipartite entanglement in phase space with controlled Gaussian unitaries
• Sufficient Wigner Negativity Implies Genuine Multipartite Entanglement
• Multipartite spatial entanglement generated by concurrent nonlinear processes
• Tripartite Entanglement in Multimode Cavity Quantum Electrodynamics
• Multipartite continuous-variable quantum nondemolition interaction and entanglement certification and monitoring
• Deterministic Generation of Genuine Tri-Partite Hybrid Atom-Photon Entanglement through Dissipation
• Multipartite entanglement in a Josephson Junction Laser