dorsal/arxiv
View SchemaThe Lorentz singular value decomposition and its applications to pure states of 3 qubits
| Authors | Frank Verstraete, Jeroen Dehaene, Bart De Moor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108043 |
| URL | https://arxiv.org/abs/quant-ph/0108043 |
| DOI | 10.1103/PhysRevA.65.032308 |
| Journal | Phys. Rev. A (\bf 65), 032308 (2002). |
Abstract
All mixed states of two qubits can be brought into normal form by the action of SLOCC operations of the kind $\rho'=(A\otimes B)\rho(A\otimes B)^\dagger$. These normal forms can be obtained by considering a Lorentz singular value decomposition on a real parameterization of the density matrix. We show that the Lorentz singular values are variationally defined and give rise to entanglement monotones, with as a special case the concurrence. Next a necessary and sufficient criterion is conjectured for a mixed state to be convertible into another specific one with a non-zero probability. Finally the formalism of the Lorentz singular value decomposition is applied to tripartite pure states of qubits. New proofs are given for the existence of the GHZ- and W-class of states, and a rigorous proof for the optimal distillation of a GHZ-state is derived.
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"abstract": "All mixed states of two qubits can be brought into normal form by the action\nof SLOCC operations of the kind $\\rho\u0027=(A\\otimes B)\\rho(A\\otimes B)^\\dagger$.\nThese normal forms can be obtained by considering a Lorentz singular value\ndecomposition on a real parameterization of the density matrix. We show that\nthe Lorentz singular values are variationally defined and give rise to\nentanglement monotones, with as a special case the concurrence. Next a\nnecessary and sufficient criterion is conjectured for a mixed state to be\nconvertible into another specific one with a non-zero probability. Finally the\nformalism of the Lorentz singular value decomposition is applied to tripartite\npure states of qubits. New proofs are given for the existence of the GHZ- and\nW-class of states, and a rigorous proof for the optimal distillation of a\nGHZ-state is derived.",
"arxiv_id": "quant-ph/0108043",
"authors": [
"Frank Verstraete",
"Jeroen Dehaene",
"Bart De Moor"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.032308",
"journal_ref": "Phys. Rev. A (\\bf 65), 032308 (2002).",
"title": "The Lorentz singular value decomposition and its applications to pure states of 3 qubits",
"url": "https://arxiv.org/abs/quant-ph/0108043"
},
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