Partial separability revisited: Necessary and sufficient criteria

Abstract

We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial separability classes in the tripartite case contrary to a former 1+8+1. Then we give necessary and sufficient criteria for these classes, which make it possible to determine to which class a mixed state belongs. These criteria are given by convex roof extensions of functions defined on pure states. In the special case of three-qubit systems, we define a different set of such functions with the help of the Freudenthal triple system approach of three-qubit entanglement.

v3: 22 pages, 5 tables, 1 figure, minor corrections (typos), clarification in the Introduction. Accepted in Phys. Rev. A. Comments are welcome

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• Entanglement patterns and generalized correlation functions in quantum many body systems
• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• Optimization of device-independent witnesses of entanglement depth from two-body correlators
• Anonymous Quantum Nonlocality
• Freudenthal Dual Lagrangians
• Entangling three identical particles via spatial overlap
• Quantum information-based analysis of electron-deficient bonds
• The classification of multipartite quantum correlation
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification
• Graph Picture of Linear Quantum Networks and Entanglement
• Extremal states of positive partial transpose in a system of three qubits
• Alternatives of entanglement depth and metrological entanglement criteria
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• Partial Multipartite Entanglement in the Matrix Product State Formalism
• Freudenthal ranks: GHZ vs. W
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• Criteria for partial entanglement of three qubit states arising from distributive rules
• Qubit entanglement: A Jordan algebraic perspective