dorsal/arxiv
View SchemaGeometric measure of entanglement and applications to bipartite and multipartite quantum states
| Authors | Tzu-Chieh Wei, Paul M. Goldbart |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307219 |
| URL | https://arxiv.org/abs/quant-ph/0307219 |
| DOI | 10.1103/PhysRevA.68.042307 |
| Journal | Phys. Rev. A 68, 042307 (2003) |
Abstract
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (see Shimony 1995 and Barnum and Linden 2001), is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states. In particular, a detailed analysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W states. Along the way, we point out connections of the geometric measure of entanglement with entanglement witnesses and with the Hartree approximation method.
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"abstract": "The degree to which a pure quantum state is entangled can be characterized by\nthe distance or angle to the nearest unentangled state. This geometric measure\nof entanglement, already present in a number of settings (see Shimony 1995 and\nBarnum and Linden 2001), is explored for bipartite and multipartite pure and\nmixed states. The measure is determined analytically for arbitrary two-qubit\nmixed states and for generalized Werner and isotropic states, and is also\napplied to certain multipartite mixed states. In particular, a detailed\nanalysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W\nstates. Along the way, we point out connections of the geometric measure of\nentanglement with entanglement witnesses and with the Hartree approximation\nmethod.",
"arxiv_id": "quant-ph/0307219",
"authors": [
"Tzu-Chieh Wei",
"Paul M. Goldbart"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.042307",
"journal_ref": "Phys. Rev. A 68, 042307 (2003)",
"title": "Geometric measure of entanglement and applications to bipartite and multipartite quantum states",
"url": "https://arxiv.org/abs/quant-ph/0307219"
},
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