Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems

Abstract

We derive inequalities sufficient to detect the genuine $N$-partite steering of $N$ distinct systems. Here, we are careful to distinguish between the concepts of full $N$-partite steering inseparability (where steering is confirmed individually for all bipartitions of the $N$ systems, thus negating the bilocal hidden state model for each bipartition) and genuine $N$-partite steering (which excludes all convex combinations of the bilocal hidden state models). Other definitions of multipartite steering are possible and we derive inequalities to detect a stricter genuine $N$-partite steering based on only one trusted site. The inequalities are expressed as variances of quadrature phase amplitudes and thus apply to continuous variable systems. We show how genuine $N$-partite steerable states can be created and detected for the nodes of a network formed from a single-mode squeezed state passed through a sequence of $N-1$ beam splitters. A stronger genuine $N$-partite steering is created, if one uses two squeezed inputs, or $N$ squeezed inputs. We are able to confirm that genuine tripartite steering (by the above definition and the stricter definition) has been realised experimentally. Finally, we analyze how bipartite steering and entanglement is distributed among the systems in the tripartite case, illustrating with monogamy inequalities. While we use Gaussian states to benchmark the criteria, the inequalities derived in this paper are not based on the assumption of Gaussian states, which gives advantage for quantum communication protocols.

References in corpus (107)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• Quantum secret sharing
• Distributed Entanglement
• Entanglement detection
• Quantum computational advantage using photons
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Device-independent security of quantum cryptography against collective attacks
• Quantum metrology with nonclassical states of atomic ensembles
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Measurement-based quantum computation
• Experimental long-lived entanglement of two macroscopic objects
• Many-particle entanglement with Bose--Einstein condensates
• Nonlinear atom interferometer surpasses classical precision limit
• No Signalling and Quantum Key Distribution
• One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
• General Monogamy Inequality for Bipartite Qubit Entanglement
• A Multiparticle Generalization of Entanglement Swapping
• From Bell's Theorem to Secure Quantum Key Distribution
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Monogamy of entanglement and other correlations
• Quantum Steering
• Multipartite entanglement for continuous variables: A quantum teleportation network
• Tripartite Quantum State Sharing
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Entanglement and Extreme Spin Squeezing
• Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb
• Detecting genuine multipartite continuous-variable entanglement
• Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
• Violation of local uncertainty relations as a signature of entanglement
• Quantification of Gaussian quantum steering
• Observation of one-way Einstein-Podolsky-Rosen steering
• Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables
• Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks
• Taming multiparticle entanglement
• Secure continuous variable quantum teleportation and Einstein-Podolsky-Rosen steering
• Bell-type inequalities to detect true n-body non-separability
• Polarization squeezing and continuous-variable polarization entanglement
• Experimental demonstration of three-color entanglement
• Device-independent witnesses of genuine multipartite entanglement
• An experimental investigation of criteria for continuous variable entanglement
• Experimental verification of a fully inseparable tripartite continuous-variable state
• Genuine multipartite Einstein-Podolsky-Rosen steering
• Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in a Bose-Einstein condensate
• Parallel generation of quadripartite cluster entanglement in the optical frequency comb
• Macroscopic quantum states: measures, fragility and implementations
• Spatially distributed multipartite entanglement enables Einstein-Podolsky-Rosen steering of atomic clouds
• Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
• The definition of multipartite nonlocality
• Bell Correlations in a Bose-Einstein Condensate
• Atomic homodyne detection of continuous variable entangled twin-atom states
• Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution
• Characterizing the entanglement of bipartite quantum systems
• Monogamy of nonlocal quantum correlations
• Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
• Three-photon energy-time entanglement
• An operational framework for nonlocality
• Programmable Multimode Quantum Networks
• Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
• Are general quantum correlations monogamous?
• General monogamy relation for the entanglement of formation in multiqubit systems
• Monogamy inequality for distributed Gaussian entanglement
• Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator
• Asymmetric Gaussian steering: when Alice and Bob disagree
• Nonlinear Bell inequalities tailored for quantum networks
• Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states
• Classifying directional Gaussian quantum entanglement, EPR steering and discord
• Monogamy inequalities for the EPR paradox and quantum steering
• Full multipartite entanglement of frequency comb Gaussian states
• Satisfying the Einstein-Podolsky-Rosen criterion with massive particles
• Experimental Characterization of Two-Particle Entanglement through Position and Momentum Correlations
• Criteria for genuine N-partite continuous variable entanglement and Einstein-Podolsky_Rosen steering
• Experimental device-independent verification of quantum steering
• Separability criterion for separate quantum systems
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox
• Metrological Detection of Multipartite Entanglement from Young Diagrams
• Einstein-Podolsky-Rosen entanglement and steering in two-well BEC ground states
• Greenberger-Horne-Zeilinger nonlocality in phase space
• Detecting faked continuous variable entanglement using one-sided device-independent entanglement witnesses
• Decoherence of Einstein-Podolsky-Rosen steering
• Continuous Variables (2,3) Threshold Quantum Secret Sharing Schemes
• Volume monogamy of quantum steering ellipsoids for multi-qubit systems
• A strong Bell correlation witness between spatially separated pairs of atoms
• Device-Independent Secret Sharing and a Stronger Form of Bell Nonlocality
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Characterizing the multipartite continuous-variable entanglement structure from squeezing coefficients and the Fisher information
• Spin entanglement, decoherence and Bohm's EPR paradox
• A Genuine Multipartite Bell Inequality for Device-independent Conference Key Agreement
• Criteria for generalized macroscopic and mesoscopic quantum coherence
• Securing quantum networking tasks with multipartite Einstein-Podolsky-Rosen steering
• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• Dynamical preparation of EPR entanglement in two-well Bose-Einstein condensates
• Entanglement, number fluctuations and optimized interferometric phase measurement
• Characterizing twin-particle entanglement in double-well potentials
• Relating spin squeezing to multipartite entanglement criteria for particles and modes
• Signifying the nonlocality of NOON states using Einstein-Podolsky-Rosen steering inequalities
• Authentication protocol based on collective quantum steering
• Number-phase entanglement and Einstein-Podolsky-Rosen steering
• Mesoscopic two-mode entangled and steerable states of 40,000 atoms in a Bose-Einstein condensate interferometer
• Criteria to detect genuine multipartite entanglement using spin measurements
• Quantum Theory and Local Hidden Variable Theory: General Features and Tests for EPR Steering
• Einstein-Podolsky-Rosen steering, depth of steering and planar spin squeezing in two-mode Bose-Einstein condensates
• Operational Characterization of Multipartite Nonlocal Correlations
• Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
• Einstein-Podolsky-Rosen-like separability indicators for two-mode Gaussian states

Cited by in corpus (11)

• Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism
• Probing quantum correlations in many-body systems: a review of scalable methods
• Simulating complex networks in phase space: Gaussian boson sampling
• Quantum squeezing induced quantum entanglement and EPR steering in coupled optomechanical system
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Minimal criteria for continuous-variable genuine multipartite entanglement
• Steady-state tripartite non-Gaussian entanglement and steering in output field from intracavity triple-photon parametric downconversion
• Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator
• Sufficient Wigner Negativity Implies Genuine Multipartite Entanglement
• Witnessing genuine multipartite entanglement in phase space with controlled Gaussian unitaries
• Multipartite continuous-variable quantum nondemolition interaction and entanglement certification and monitoring