A geometric formulation to measure global and genuine entanglement in three-qubit systems

Abstract

We introduce a purely geometric formulation for two different measures addressed to quantify the entanglement between different parts of a tripartite qubit system. Our approach considers the entanglement-polytope defined by the smallest eigenvalues of the reduced density matrices of the qubit-components. The measures identify global and genuine entanglement, and are respectively associated with the projection and rejection of a given point of the polytope on the corresponding biseparable segments. Solving the so called `inverse problem', we also discuss a way to force the system to behave in a particular form, which opens the possibility of controlling and manipulating entanglement for practical purposes.

22+5 pages, 11+2 figures, 1 table. We have added an appendix with detailed information about the classification of three-qubit states in standard form (it includes 3 new tables). Some additional references are also included

References in corpus (7)

• Taming multiparticle entanglement
• Measure of genuine multipartite entanglement with computable lower bounds
• A classification of entanglement in three-qubit systems
• The maximally entangled symmetric state in terms of the geometric measure
• A Triangle Governs Genuine Tripartite Entanglement
• Asymptotic properties of entanglement polytopes for large number of qubits
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Cited by in corpus (2)

• Three-Qubit State Preparation: Classification and Explicit Circuits
• Optimizing entanglement in two-qubit systems