Structural Quantification of Entanglement

Abstract

We introduce an approach which allows a detailed structural and quantitative analysis of multipartite entanglement. The sets of states with different structures are convex and nested. Hence, they can be distinguished from each other using appropriate measurable witnesses. We derive equations for the construction of optimal witnesses and discuss general properties arising from our approach. As an example, we formulate witnesses for a 4-cluster state and perform a full quantitative analysis of the entanglement structure in the presence of noise and losses. The strength of the method in multimode continuous variable systems is also demonstrated by considering a dephased GHZ-type state.

12 pages, 1 table and 3 figures

References in corpus (40)

• Quantum entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Three qubits can be entangled in two inequivalent ways
• Entanglement detection
• Quantifying Entanglement
• Measurement-based quantum computation with cluster states
• Entanglement Measures and Purification Procedures
• Nonlinear atom interferometer surpasses classical precision limit
• Bell Inequalities and the Separability Criterion
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Optimization of entanglement witnesses
• Robustness of entanglement
• Multipartite entanglement for continuous variables: A quantum teleportation network
• Wavelength-Multiplexed Quantum Networks with Ultrafast Frequency Combs
• Detecting genuine multipartite continuous-variable entanglement
• A Schmidt number for density matrices
• Most quantum states are too entangled to be useful as computational resources
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Schmidt number witnesses and bound entanglement
• The structure of multidimensional entanglement in multipartite systems
• Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps
• Entanglement quantification and purification in continuous variable systems
• Quantum Hypergraph States
• How robust is a quantum gate in the presence of noise?
• Multipartite Entanglement Witnesses
• Extracting entanglement from identical particles
• The maximally entangled set of multipartite quantum states
• Observation of squeezed states with strong photon number oscillations
• Quantification and scaling of multipartite entanglement in continuous variable systems
• Necessary and sufficient conditions for bipartite entanglement
• Hierarchies of multi-partite entanglement
• Determination of the Schmidt number
• Multipartite continuous-variable entanglement
• Experimental test of nonclassicality criteria
• Entanglement for multipartite systems of indistinguishable particles
• A quantitative witness for Greenberger-Horne-Zeilinger entanglement
• Entanglement quasiprobabilities of squeezed light
• Operational Gaussian Schmidt-Number Witnesses
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication

Cited by in corpus (26)

• Quantum Resource Theories
• Detecting multipartite entanglement structure with minimal resources
• Is "genuine multipartite entanglement" really genuine?
• Characterizing multipartite entanglement classes via higher-dimensional embeddings
• Entanglement Witnesses for Indistinguishable Particles
• Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement
• Measurement-Device-Independent Approach to Entanglement Measures
• Entanglement in macroscopic systems
• Design and Experimental Performance of Local Entanglement Witness Operators
• Mode-independent quantum entanglement for light
• Entanglement and nonclassicality: A mutual impression
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• Numerical construction of multipartite entanglement witnesses
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits
• Quantum correlations in composite systems
• Efficient measurement-device-independent detection of multipartite entanglement structure
• Quantum coherences of indistinguishable particles
• Entangled states in the role of witnesses
• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• Simulating quantum instruments with projective measurements and quantum post-processing
• Entanglement between dependent degrees of freedom: Quasiparticle correlations
• Variational-toolbox-based separability detection of multiqubit states
• Entanglement Structure Certification Based on Energy-Restricted State Discrimination
• Entanglement Meter: Estimation of entanglement with single copy in Interferometer
• Universal entanglement detection with geometrically optimal witnesses
• Preservation of dynamics in coupled cavity system using second order nonlinearity