dorsal/arxiv
View SchemaFour qubits can be entangled in nine different ways
| Authors | F. Verstraete, J. Dehaene, B. De Moor, H. Verschelde |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109033 |
| URL | https://arxiv.org/abs/quant-ph/0109033 |
| DOI | 10.1103/PhysRevA.65.052112 |
| Journal | Phys. Rev. A, 65: 052112 (2002). |
Abstract
We consider a single copy of a pure four-partite state of qubits and investigate its behaviour under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four-qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to GHZ-like entanglement. The other ones contain essentially 2- or 3-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of 4 qubits, giving rise to a seven parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single copy distillation protocol.
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"abstract": "We consider a single copy of a pure four-partite state of qubits and\ninvestigate its behaviour under the action of stochastic local quantum\noperations assisted by classical communication (SLOCC). This leads to a\ncomplete classification of all different classes of pure states of four-qubits.\nIt is shown that there exist nine families of states corresponding to nine\ndifferent ways of entangling four qubits. The states in the generic family give\nrise to GHZ-like entanglement. The other ones contain essentially 2- or 3-qubit\nentanglement distributed among the four parties. The concept of concurrence and\n3-tangle is generalized to the case of mixed states of 4 qubits, giving rise to\na seven parameter family of entanglement monotones. Finally, the SLOCC\noperations maximizing all these entanglement monotones are derived, yielding\nthe optimal single copy distillation protocol.",
"arxiv_id": "quant-ph/0109033",
"authors": [
"F. Verstraete",
"J. Dehaene",
"B. De Moor",
"H. Verschelde"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.052112",
"journal_ref": "Phys. Rev. A, 65: 052112 (2002).",
"title": "Four qubits can be entangled in nine different ways",
"url": "https://arxiv.org/abs/quant-ph/0109033"
},
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