Bogdan A Bernevig and Han-Dong Chen 2003 J. Phys. A: Math. Gen. 36 8325 doi:10.1088/0305-4470/36/30/309
Bogdan A Bernevig1 and Han-Dong Chen2
Show affiliationsWe 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 Hilbert space of the three-qubit system is the 15-dimensional sphere S15, which allows for a natural (last) Hopf fibration with S8 as base and S7 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.
03.67.Lx Quantum computation architectures and implementations
03.67.Mn Entanglement measures, witnesses, and other characterizations
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
Issue 30 (1 August 2003)
Received 11 February 2003, in final form 3 June 2003
Published 16 July 2003
Bogdan A Bernevig and Han-Dong Chen 2003 J. Phys. A: Math. Gen. 36 8325
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