Geometry of three-qubit entanglement

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A geometrical description of three-qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric Q, a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of Q with interesting geometric properties. An invariant characterizing the Greenberger-Horne-Zeilinger class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.

Original languageEnglish
Article number012334
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number1
Publication statusPublished - Jan 1 2005


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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