Examining the dimensionality of genuine multipartite entanglement

Abstract

Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize multipartite states by the number of degrees of freedom being entangled. In this regard, we derive computable and experimentally friendly criteria for arbitrary multipartite qudit systems that enable to examine in how many degrees of freedom a mixed state is genuine multipartite entangled.

8 pages, 2 figures, v3 as published; Quantum Information Processing (2012)

References in corpus (15)

• Entanglement detection
• Taming multiparticle entanglement
• Measure of genuine multipartite entanglement with computable lower bounds
• Quantum secret sharing with qudit graph states
• Quantum Error Correcting Codes Using Qudit Graph States
• Nonlocality and entanglement in a strange system
• Generalized W-Class State and its Monogamy Relation
• Experimentally Feasible Security Check for n-qubit Quantum Secret Sharing
• A composite parameterization of unitary groups, density matrices and subspaces
• Composite parameterization and Haar measure for all unitary and special unitary groups
• The Decay of Multiqudit Entanglement
• Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions
• Verifying Genuine High-Order Entanglement
• Experimentally implementable criteria revealing substructures of genuine multipartite entanglement
• A Computable Criterion for Partial Entanglement in Continuous Variable Quantum Systems

Cited by in corpus (15)

• Entanglement detection via mutually unbiased bases
• The structure of multidimensional entanglement in multipartite systems
• The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
• Determining lower bounds on a measure of multipartite entanglement from few local observables
• Entangled Singularity patterns of Photons in Ince-Gauss modes
• Characterizing multipartite entanglement without shared reference frames
• Characterizing finite-dimensional quantum behavior
• Deformations of Polyhedra and Polygons by the Unitary Group
• Analysing quantum systems with randomised measurements
• Separability conditions based on local fine-grained uncertainty relations
• Criteria to detect genuine multipartite entanglement using spin measurements
• Detecting the dimensionality of genuine multi-particle entanglement
• Entropy and complexity properties of the d-dimensional blackbody radiation
• Biparametric complexities and the generalized Planck radiation law
• Rényi and Tsallis formulations of separability conditions in finite dimensions