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.
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|Publication status||Published - Jan 1 2005|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics