### Abstract

We present a generalization to three qubits of the standard Bloch sphere representation for a single qubit and of the seven-dimensional sphere representation for two qubits presented in Mosseri et al (Mosseri R and Dandoloff R 2001 J. Phys. A: Math. Gen. 34 10243). The Hubert space of the three-qubit system is the 15-dimensional sphere S^{15}, which allows for a natural (last) Hopf fibration with S^{8} as base and S ^{7} as fibre. A striking feature is, as in the case of one and two qubits, that the map is entanglement sensitive, and the two distinct ways of un-entangling three qubits are naturally related to the Hopf map. We define a quantity that measures the degree of entanglement of the three-qubit state. Conjectures on the possibility of generalizing the construction for higher qubit states are also discussed.

Original language | English (US) |
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Pages (from-to) | 8325-8339 |

Number of pages | 15 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 30 |

DOIs | |

State | Published - Aug 1 2003 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and General*,

*36*(30), 8325-8339. https://doi.org/10.1088/0305-4470/36/30/309