Universal Measure of Entanglement

Abstract

A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined separable state with the same marginals. A generalization of the Schmidt decomposition is developed to implement the separation of correlations for any pure, multipartite state. The measure based on this decomposition is a generalization of the entanglement of formation to multipartite systems, provides an upper bound for the relative entropy of entanglement, and is directly computable on pure states. The example of pure three-qubit states is analyzed in detail, and a classification based on minimal, four-term decompositions is developed.

4 pages

References in corpus (11)

• Mixed State Entanglement and Quantum Error Correction
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Entanglement Measures and Purification Procedures
• The Role of Relative Entropy in Quantum Information Theory
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Limits for entanglement measures
• Collective tests for quantum nonlocality
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• Remarks on entanglement measures and non-local state distinguishability
• Parametrization and distillability of three-qubit entanglement

Cited by in corpus (13)

• Generalized information theoretic measure to discern the quantumness of correlations
• An Introduction to Quantum Entanglement: a Geometric Approach
• Glimmers of a pre-geometric perspective
• A Note on Entanglement of Formation and Generalized Concurrence
• Free Entanglement Measure
• Classification of Tripartite Entanglement with one Qubit
• Extremal Entanglement For Triqubit Pure States
• Entanglement measure for general pure multipartite quantum states
• Combinatorial Approaches in Quantum Information Theory
• Compatibility Relations between the Reduced and Global Density Matrixes
• Geometric measures of entanglement and the Schmidt decomposition
• A combinatorial approach for studying LOCC transformations of multipartite states
• Mixing Property of Quantum Relative Entropy