### Abstract

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 language | English |
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Article number | 012334 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 71 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2005 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics