Optimal entanglement witnesses for continuous-variable systems
arXiv:quant-ph/0510077 · doi:10.1088/1367-2630/8/4/051
Abstract
This paper is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All such tests for bi-partite and multi-partite entanglement correspond to hyperplanes in the set of second moments. It is shown that all optimal tests, those that are most robust against imperfections with respect to some figure of merit for a given state, can be constructed from solutions to semi-definite optimization problems. Moreover, we show that for each such test, referred to as entanglement witness based on second moments, there is a one-to-one correspondence between the witness and a stronger product criterion, which amounts to a non-linear witness, based on the same measurements. This generalizes the known product criteria. The presented tests are all applicable also to non-Gaussian states. To provide a service to the community, we present the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have been made publicly available.
14 pages LaTeX, 1 figure, presentation improved, references updated
References in corpus (49)
- A computable measure of entanglement
- Quantum information with continuous variables
- Separability of Mixed States: Necessary and Sufficient Conditions
- Peres-Horodecki separability criterion for continuous variable systems
- Inseparability criterion for continuous variable systems
- The logarithmic negativity: A full entanglement monotone that is not convex
- On the volume of the set of mixed entangled states
- Experimental long-lived entanglement of two macroscopic objects
- Experimental demonstration of quantum memory for light
- Bell Inequalities and the Separability Criterion
- Optimization of entanglement witnesses
- Extremal entanglement and mixedness in continuous variable systems
- On the impossibility of distilling Gaussian states with Gaussian operations
- Classification of mixed three-qubit states
- The characterization of Gaussian operations and Distillation of Gaussian States
- Multipartite entanglement for continuous variables: A quantum teleportation network
- Detecting genuine multipartite continuous-variable entanglement
- Bound entangled Gaussian states
- A complete family of separability criteria
- Gaussian transformations and distillation of entangled Gaussian states
- Entanglement conditions for two-mode states
- Generation of Continuous Variable Einstein-Podolsky-Rosen Entanglement via the Kerr Nonlinearity in an Optical Fibre
- Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables
- Inseparability criteria for bipartite quantum states
- Quantum State Transfer Between Matter and Light
- Entanglement of formation for symmetric Gaussian states
- Extremality of Gaussian quantum states
- Classification of multi-qubit mixed states: separability and distillability properties
- The entanglement cost under operations preserving the positivity of partial transpose
- Separability and distillability of multiparticle quantum systems
- Experimental verification of a fully inseparable tripartite continuous-variable state
- Experimental Demonstration of Unconditional Entanglement Swapping for Continuous Variables
- Characterizing the entanglement of bipartite quantum systems
- Separability Properties of Three-mode Gaussian States
- Optimal teleportation with a mixed state of two qubits
- Unconditional teleportation of continuous-variable entanglement
- Inseparability inequalities for higher-order moments for bipartite systems
- Determination of continuous variable entanglement by purity measurements
- Narrowband frequency tunable light source of continuous quadrature entanglement
- On the quantification of entanglement in infinite-dimensional quantum systems
- Complete hierarchies of efficient approximations to problems in entanglement theory
- A characterization of continuous variable entanglement
- Finding optimal strategies for minimum-error quantum-state discrimination
- Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
- How to measure squeezing and entanglement of Gaussian states without homodyning
- Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state
- Experimental Generation of Large Quadrature EPR Entanglement with a Self-Phase-Locked Type II OPO Below Threshold
- Optimizing linear optics quantum gates
- Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable
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- Tripartite separability conditions exponentially violated by Gaussian states
- Restricted Monte Carlo wave function method and Lindblad equation for identifying entangling open-quantum-system dynamics
- Multi-copy activation of genuine multipartite entanglement in continuous-variable systems
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- Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability
- Revisiting Gaussian genuine entanglement witnesses with modern software