Practical method to obtain a lower bound to the three-tangle

Abstract

The quantitative assessment of the entanglement in multipartite quantum states is, apart from its fundamental importance, a practical problem. Recently there has been significant progress in developing new methods to determine certain entanglement measures. In particular, there is a method---in principle, analytical---to compute a certified lower bound for the three-tangle. The purpose of this work is to provide a manual for the implementation of this approach and to explicitly discuss several analytically solvable cases in order to gauge the numerical tools. Moreover, we derive a simple analytical bound for the mixed state three-tangle.

9 pages, 4 figures, typo in important Eq (14) corrected, section on tomography added

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Cited by in corpus (15)

• Quantifying entanglement resources
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• The rebit three-tangle and its relation to two-qubit entanglement
• Evaluating the geometric measure of multiparticle entanglement
• Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement
• Evaluation of entanglement measures by a single observable
• Geometric approach to entanglement quantification with polynomial measures
• Generalized W-state of four qubits with exclusively threetangle
• Triangle inequalities in coherence measures and entanglement concurrence
• Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy
• Upper bound for SL-invariant entanglement measures of mixed states
• Upper bound on three tangles of reduced states of four-qubit pure states
• Entanglement Classification of Restricted Greenberger-Horne-Zeilinger Symmetric States in Four-Qubit System
• Threetangle in the XY-model class with a non-integrable field background
• Maximum residual strong monogamy inequality for multiqubit entanglement