Hypergraph-theoretic charaterizations for LOCC incomparable ensembles of multipartite CAT states

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dc.creatorGhosh, Arijit
dc.creatorPal, Sudebkumar Prasant
dc.creatorPrakash, Anupam
dc.creatorShekhawat, Virendra Singh
dc.date2007-09-01
dc.date2007-10-23
dc.date.accessioned2026-07-07T08:37:30Z
dc.date.available2026-07-07T08:37:30Z
dc.descriptionUsing graphs and hypergraphs to systematically model collections of arbitrary subsets of parties representing {\it ensembles (or collections)} of shared multipartite CAT states, we study transformations between such {\it ensembles} under {\it local operations and classical communication (LOCC)}. We show using partial entropic criteria, that any two such distinct ensembles represented by {\it $r$-uniform hypergraphs} with the same number of hyperedges (CAT states), are LOCC incomparable for even integers $r\geq 2$, generalizing results in \cite{mscthesis,sin:pal:kum:sri}. We show that the cardinality of the largest set of mutually LOCC incomparable ensembles represented by $r$-uniform hypergraphs for even $r\geq 2$, is exponential in the number of parties. We also demonstrate LOCC incomparability between two ensembles represented by 3-uniform hypergraphs where partial entropic criteria do not help in establishing incomparability. Further we characterize LOCC comparability of EPR graphs in a model where LOCC is restricted to teleportation and edge destruction. We show that this model is equivalent to one in which LOCC transformations are carried out through a sequence of operations where each operation adds at most one new EPR pair.
dc.description13 pages, 4 figures, presented in AQIS 2007
dc.identifierhttps://arxiv.org/abs/0709.0063
dc.identifierhttp://arxiv.org/abs/0709.0063
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140420
dc.subjectQuantum Physics
dc.titleHypergraph-theoretic charaterizations for LOCC incomparable ensembles of multipartite CAT states
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