Parametrization and distillability of three-qubit entanglement

Abstract

There is an ongoing effort to quantify entanglement of quantum pure states for systems with more than two subsystems. We consider three approaches to this problem for three-qubit states: choosing a basis which puts the state into a standard form, enumerating ``local invariants,'' and using operational quantities such as the number of maximally entangled states which can be distilled. In this paper we evaluate a particular standard form, the {\it Schmidt form}, which is a generalization of the Schmidt decomposition for bipartite pure states. We show how the coefficients in this case can be parametrized in terms of five physically meaningful local invariants; we use this form to prove the efficacy of a particular distillation technique for GHZ triplets; and we relate the yield of GHZs to classes of states with unusual entanglement properties, showing that these states represent extremes of distillability as functions of two local invariants.

17 pages RevTeX 3.0 including 2 figures (encapsulated Postscript) Final version, to appear in Physics Letters A

References in corpus (8)

• Three qubits can be entangled in two inequivalent ways
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• How entangled can two couples get?
• Multipartite generalisation of the Schmidt decomposition
• On local invariants of pure three-qubit states
• Local symmetry properties of pure 3-qubit states
• Optimal distillation of a GHZ state
• Distillation of GHZ states by selective information manipulation

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• An Introduction to Quantum Entanglement: a Geometric Approach
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