A quantitative witness for Greenberger-Horne-Zeilinger entanglement

Abstract

Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger--type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result [Phys. Rev. Lett. 80, 2245 (1998)]. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.

References in corpus (6)

• Entanglement detection
• Estimating entanglement measures in experiments
• Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Three-tangle for mixtures of generalized GHZ and generalized W states
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• Quantifying mixed-state quantum entanglement by optimal entanglement witness

Cited by in corpus (20)

• Quantifying entanglement resources
• Dynamical Casimir effect entangles artificial atoms
• Evaluation of convex roof entanglement measures
• The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• Structural Quantification of Entanglement
• Strong monogamy inequalities for four qubits
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• Quantifying entanglement of maximal dimension in bipartite mixed states
• Practical method to obtain a lower bound to the three-tangle
• Approaches to Measuring Entanglement in Chemical Magnetometers
• Accessible quantification of multiparticle entanglement
• Entanglement Classification via Witness Operators generated by Support Vector Machine
• Geometric approach to entanglement quantification with polynomial measures
• Generalized W-state of four qubits with exclusively threetangle
• Accessible bounds for general quantum resources
• A heat bath can generate all classes of three-qubit entanglement
• Bounding the entanglement of N qubits with only four measurements
• Upper bound for SL-invariant entanglement measures of mixed states
• Threetangle in the XY-model class with a non-integrable field background