Three qubits can be entangled in two inequivalent ways

Dur, W., Vidal, G. and Cirac, J. I. (2000) Three qubits can be entangled in two inequivalent ways. Physical Review a, 62 6: 062314-062311. doi:10.1103/PhysRevA.62.062314

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Author Dur, W.
Vidal, G.
Cirac, J. I.
Title Three qubits can be entangled in two inequivalent ways
Journal name Physical Review a   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 2000-12-01
Sub-type Article (original research)
DOI 10.1103/PhysRevA.62.062314
Open Access Status File (Publisher version)
Volume 62
Issue 6
Start page 062314
End page 062311
Total pages 12
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Formatted abstract
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the Greenberger-Horne-Zeilinger state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher-dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success.
Keyword Multiparticle Entanglement
States
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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