TY - JOUR
T1 - Quantum perfect state transfer on weighted join graphs
AU - Angeles-Canul, Ricardo Javier
AU - Norton, Rachael M.
AU - Opperman, Michael C.
AU - Paribello, Christopher C.
AU - Russell, Matthew C.
AU - Tamon, Christino
N1 - Funding Information:
This research was supported by the National Science Foundation grant DMS-0646847 and the National Security Agency grant H98230-09-1-0098.
PY - 2009/12
Y1 - 2009/12
N2 - 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
AB - 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
KW - Join
KW - Perfect state transfer
KW - Quantum networks
KW - Weighted graphs
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U2 - 10.1142/S0219749909006103
DO - 10.1142/S0219749909006103
M3 - Article
AN - SCOPUS:76449098466
VL - 7
SP - 1429
EP - 1445
JO - International Journal of Quantum Information
JF - International Journal of Quantum Information
SN - 0219-7499
IS - 8
ER -