dorsal/arxiv
View SchemaGeometry of the 3-Qubit State, Entanglement and Division Algebras
| Authors | Bogdan A. Bernevig, Han-Dong Chen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302081 |
| URL | https://arxiv.org/abs/quant-ph/0302081 |
| DOI | 10.1088/0305-4470/36/30/309 |
| Journal | J. Phys. A: Math. Gen., 36, 8325 (2003) |
Abstract
We present a generalization to 3-qubits of the standard Bloch sphere representation for a single qubit and of the 7-dimensional sphere representation for 2 qubits presented in Mosseri {\it et al.}\cite{Mosseri2001}. The Hilbert space of the 3-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 fiber. A striking feature is, as in the case of 1 and 2 qubits, that the map is entanglement sensitive, and the two distinct ways of un-entangling 3 qubits are naturally related to the Hopf map. We define a quantity that measures the degree of entanglement of the 3-qubit state. Conjectures on the possibility to generalize the construction for higher qubit states are also discussed.
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"abstract": "We present a generalization to 3-qubits of the standard Bloch sphere\nrepresentation for a single qubit and of the 7-dimensional sphere\nrepresentation for 2 qubits presented in Mosseri {\\it et\nal.}\\cite{Mosseri2001}. The Hilbert space of the 3-qubit system is the\n15-dimensional sphere $S^{15}$, which allows for a natural (last) Hopf\nfibration with $S^8$ as base and $S^7$ as fiber. A striking feature is, as in\nthe case of 1 and 2 qubits, that the map is entanglement sensitive, and the two\ndistinct ways of un-entangling 3 qubits are naturally related to the Hopf map.\nWe define a quantity that measures the degree of entanglement of the 3-qubit\nstate. Conjectures on the possibility to generalize the construction for higher\nqubit states are also discussed.",
"arxiv_id": "quant-ph/0302081",
"authors": [
"Bogdan A. Bernevig",
"Han-Dong Chen"
],
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"quant-ph"
],
"doi": "10.1088/0305-4470/36/30/309",
"journal_ref": "J. Phys. A: Math. Gen., 36, 8325 (2003)",
"title": "Geometry of the 3-Qubit State, Entanglement and Division Algebras",
"url": "https://arxiv.org/abs/quant-ph/0302081"
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