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http://hdl.handle.net/2289/1911
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 combinatorics hypergraphs 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 |
URI: | http://hdl.handle.net/2289/1911 |
ISBN: | 0735403627 |
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) |
Files in This Item:
File | Description | Size | Format | |
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2006 AIP Conf p156-170.pdf | Open Access | 133.9 kB | Adobe PDF | View/Open |
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