QUANTUM PERFECT STATE TRANSFER ON WEIGHTED JOIN GRAPHS

Author:

ANGELES-CANUL RICARDO JAVIER1,NORTON RACHAEL M.2,OPPERMAN MICHAEL C.3,PARIBELLO CHRISTOPHER C.4,RUSSELL MATTHEW C.5,TAMON CHRISTINO6

Affiliation:

1. Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, Pachuca, Hidalgo, Mexico

2. Department of Mathematics, Bowdoin College, 8600 College Station, Brunswick, ME 04011-8486, USA

3. Department of Mathematics, Clarkson University, 8 Clarkson Avenue, Potsdam, NY 13699-5815, USA

4. Division of Mathematics and Computer Science, Clarkson University, 8 Clarkson Avenue, Potsdam, NY 13699-5815, USA

5. Department of Mathematics, Taylor University, 236 West Reade Avenue, Upland, IN 46989-1001, USA

6. Department of Computer Science, Clarkson University, 8 Clarkson Avenue, Potsdam, NY 13699-5815, USA

Abstract

This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al.1 where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph has perfect state transfer between each pair of its vertices. The result is a corollary of a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on a hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes, thus generalizing results of Bernasconi et al.2 and Moore and Russell.3

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

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