On quantum perfect state transfer in weighted join graphs - Quantum PhysicsReport as inadecuate

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Abstract: We study perfect state transfer on quantum networks represented by weightedgraphs. Our focus is on graphs constructed from the join and related graphoperators. Some specific results we prove include: 1 The join of a weightedtwo-vertex graph with any regular graph has perfect state transfer. Thisgeneralizes a result of Casaccino et al. clms09 where the regular graph is acomplete graph or a complete graph with a missing link. In contrast, thehalf-join of a weighted two-vertex graph with any weighted regular graph has noperfect state transfer. This implies that adding weights in a completebipartite graph do not help in achieving perfect state transfer. 2 A Hamminggraph has perfect state transfer between each pair of its vertices. This isobtained using a closure property on weighted Cartesian products of perfectstate transfer graphs. Moreover, on the hypercube, we show that perfect statetransfer occurs between uniform superpositions on pairs of arbitrary subcubes.This generalizes results of Bernasconi et al. bgs08 and Moore and Russellmr02. Our techniques rely heavily on the spectral properties of graphs builtusing the join and Cartesian product operators.

Author: R.J. Angeles-Canul, R. Norton, M. Opperman, C. Paribello, M. Russell, C. Tamon

Source: https://arxiv.org/

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