Two computable sets of multipartite entanglement measures

Abstract

We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are separable/entangled. For that we have to extend the concept of k-separability for multipartite systems to a novel unambiguous separability concept which we call γ_k-separability. The second set of entanglement measures reveals the 'kind' of entanglement, i.e. if it is bipartite, tripartite, ..., n-partite entangled and is denoted as the 'physical' measure. We show how lower bounds on both sets of measures can be obtained by the observation that any entropy may be rewritten via operational expressions known as m-concurrences. Moreover, for different classes of bipartite or multipartite qudit systems we compute the bounds explicitly and discover that they are often tight or equivalent to positive partial transposition (PPT).

3 figures, 21 pages

References in corpus (36)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• Quantifying Entanglement
• Entanglement Measures and Purification Procedures
• Universal state inversion and concurrence in arbitrary dimensions
• Four qubits can be entangled in nine different ways
• Global entanglement in multiparticle systems
• Characterizing Entanglement
• The Bloch Vector for N-Level Systems
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Fidelity and Concurrence of conjugated states
• Measures and dynamics of entangled states
• Bloch vectors for qudits
• A subsystem-independent generalization of entanglement
• Normal forms and entanglement measures for multipartite quantum states
• Multi-particle entanglement and its applications to cryptography
• Quantum Communication between N partners and Bell's inequalities
• A four-party unlockable bound-entangled state
• Variational Characterisations of Separability and Entanglement of Formation
• The state space for two qutrits has a phase space structure in its core
• Nature and Measure of Entanglement in Quantum Phase Transitions
• A special simplex in the state space for entangled qudits
• Bound entanglement maximally violating Bell inequalities: quantum entanglement is not equivalent to quantum security
• The geometry of bipartite qutrits including bound entanglement
• Nonlocality and entanglement in a strange system
• Bell inequality and CP violation in the neutral kaon system
• Operational Classification and Quantification of Multipartite Entangled States
• Multipartite entanglement measure for all discrete systems
• Multipartite Classical and Quantum Secrecy Monotones
• Evaluable multipartite entanglement measures: are multipartite concurrences entanglement monotones?
• Quantum communication cost of preparing multipartite entanglement
• A simplex of bound entangled multipartite qubit states

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• Purification of genuine multipartite entanglement
• Genuine Multipartite Entanglement in the $XY$ Model
• Is "genuine multipartite entanglement" really genuine?
• Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure
• A family of multipartite separability criteria based on correlation tensor
• A composite parameterization of unitary groups, density matrices and subspaces
• Composite parameterization and Haar measure for all unitary and special unitary groups
• Experimentally implementable criteria revealing substructures of genuine multipartite entanglement
• Lorentz invariance of entanglement classes in multipartite systems
• Proving the Generation of Genuine Multipartite Entanglement in a Single-Neutron Interferometer Experiment
• A geometric comparison of entanglement and quantum nonlocality in discrete systems
• Hierarchy of multipartite nonlocality in the nonsignaling scenario
• Bipartite Bound Entanglement
• Criteria for reliable entanglement quantification with finite data
• Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States
• Two distinct classes of bound entanglement: PPT-bound and `multi-particle'-bound
• Twin GHZ-states behave differently
• Mixed State Entanglement Measures for Intermediate Separability