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Title: Entangled graphs: Bipartite entanglement in multiqubit systems

Abstract

Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits, we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite system is associated with a point (vertex), while a bipartite entanglement between two specific qubits is represented by a connection (edge) between these points. We prove that any such entangled structure can be associated with a pure state of a multiqubit system. Moreover, we show that a pure state corresponding to a given entangled structure is a superposition of vectors from a subspace of the 2{sup N}-dimensional Hilbert space, whose dimension grows linearly with the number of entangled pairs.

Authors:
 [1];  [1]
  1. Research Center for Quantum Information, Slovak Academy of Sciences, Dubravska cesta 9, Bratislava (Slovakia)
Publication Date:
OSTI Identifier:
20634100
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 67; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.67.012322; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; CORRELATIONS; ENERGY LEVELS; HILBERT SPACE; INFORMATION THEORY; QUANTUM MECHANICS; VECTORS

Citation Formats

Plesch, Martin, Buzek, Vladimir, and Department of Mathematical Physics, National University of Ireland, Maynooth, Co. Kildare. Entangled graphs: Bipartite entanglement in multiqubit systems. United States: N. p., 2003. Web. doi:10.1103/PhysRevA.67.012322.
Plesch, Martin, Buzek, Vladimir, & Department of Mathematical Physics, National University of Ireland, Maynooth, Co. Kildare. Entangled graphs: Bipartite entanglement in multiqubit systems. United States. https://doi.org/10.1103/PhysRevA.67.012322
Plesch, Martin, Buzek, Vladimir, and Department of Mathematical Physics, National University of Ireland, Maynooth, Co. Kildare. 2003. "Entangled graphs: Bipartite entanglement in multiqubit systems". United States. https://doi.org/10.1103/PhysRevA.67.012322.
@article{osti_20634100,
title = {Entangled graphs: Bipartite entanglement in multiqubit systems},
author = {Plesch, Martin and Buzek, Vladimir and Department of Mathematical Physics, National University of Ireland, Maynooth, Co. Kildare},
abstractNote = {Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits, we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite system is associated with a point (vertex), while a bipartite entanglement between two specific qubits is represented by a connection (edge) between these points. We prove that any such entangled structure can be associated with a pure state of a multiqubit system. Moreover, we show that a pure state corresponding to a given entangled structure is a superposition of vectors from a subspace of the 2{sup N}-dimensional Hilbert space, whose dimension grows linearly with the number of entangled pairs.},
doi = {10.1103/PhysRevA.67.012322},
url = {https://www.osti.gov/biblio/20634100}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 67,
place = {United States},
year = {Wed Jan 01 00:00:00 EST 2003},
month = {Wed Jan 01 00:00:00 EST 2003}
}