Quantum perfect state transfer on weighted join graphs

Ricardo Javier Angeles-Canul, Rachael M. Norton, Michael C. Opperman, Christopher C. Paribello, Matthew C. Russell, Christino Tamon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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

Original languageEnglish (US)
Pages (from-to)1429-1445
Number of pages17
JournalInternational Journal of Quantum Information
Issue number8
StatePublished - Dec 2009


  • Join
  • Perfect state transfer
  • Quantum networks
  • Weighted graphs

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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