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 (24)

• Entanglement detection
• Quantum computational advantage using photons
• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Nonlinear atom interferometer surpasses classical precision limit
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Quantification of Gaussian quantum steering
• Observation of one-way Einstein-Podolsky-Rosen steering
• Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks
• Taming multiparticle entanglement
• Experimental demonstration of three-color entanglement
• Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
• Monogamy inequality for distributed Gaussian entanglement
• Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator
• Classifying directional Gaussian quantum entanglement, EPR steering and discord
• Full multipartite entanglement of frequency comb Gaussian states
• Experimental device-independent verification of quantum steering
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• Metrological Detection of Multipartite Entanglement from Young Diagrams
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Criteria for generalized macroscopic and mesoscopic quantum coherence
• Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states

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• 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