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|Title: ||Multipartite entanglement configurations: Combinatorial offshoots into (hyper) graph theory and their ramifications|
|Authors: ||Pal, Sudebkumar Prasant|
|Keywords: ||entanglement characterization and manipulation|
|Issue Date: ||Dec-2006 |
|Publisher: ||American Institute of Physics|
|Citation: ||AIP Conference Proceedings Vol.864 on Quantum Computing, 2006, p156-170|
|Abstract: ||Computations in a distributed environment comprising a network of spatially separated
nodes may require the exchange of classical and quantum information. The amount of classical
communication may be reduced in such computations by using multipartite entanglement. Following
the combinatorial approach developed in [25, 27], we study entanglement configurations over
a set of nodes, where each entanglement configuration is a collection of multipartite entanglement
(CAT or GHZ) states shared within different combinations of subsets of nodes. The main problem
is to determine whether LOCC transformations can generate an entanglement configuration B from
another entanglement configuration A, written as B _LOCC A. We characterize the resulting partial
order introduced on unitarily equivalent classes of entanglement configurations due to LOCC transformations.
This study includes the communication complexity of generating higher cardinality
multipartite CAT states from smaller sized CAT state configurations. We also study classes of incomparable
entanglement configurations where no pair _A_B_ of configurations satisfies A_LOCC B.
This leads us to investigate certain combinatorial properties of hypergraphs and hypertrees following
initial results in [25, 27].We study the unique reconstruction of vertex labelled r-uniform hypertrees
on n vertices, where r _ n is a constant, and each hyperedge has the same number r, of vertices.
We conclude by discussing several problems and open questions in the context of entanglement
|Description: ||Paper presented at the AIP conference proceedings Vol.864 on Quantum Computing: Back action, edited by D. Goswami, held at IIT Kanpur, March 5-12, 2006.|
|Alternative Location: ||http://dx.doi.org/10.1063/1.2400887|
|Copyright: ||2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.|
|Appears in Collections:||Research Papers (LAMP)|
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