Please use this identifier to cite or link to this item:
Title: Multipartite entanglement configurations: Combinatorial offshoots into (hyper) graph theory and their ramifications
Authors: Pal, Sudebkumar Prasant
Kumar, Somesh
Srikanth, R.
Keywords: entanglement characterization and manipulation
entanglement configurations
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 configurations.
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.
Open Access
ISBN: 0735403627
Alternative Location:
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)

Files in This Item:
File Description SizeFormat 
2006 AIP Conf p156-170.pdfOpen Access133.9 kBAdobe PDFView/Open

Items in RRI Digital Repository are protected by copyright, with all rights reserved, unless otherwise indicated.