Pretty good state transfer in discrete-time quantum walks
- URL: http://arxiv.org/abs/2105.03762v1
- Date: Sat, 8 May 2021 18:55:57 GMT
- Title: Pretty good state transfer in discrete-time quantum walks
- Authors: Ada Chan, Hanmeng Zhan
- Abstract summary: We establish the theory for pretty good state transfer in discrete-time quantum walks.
For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We establish the theory for pretty good state transfer in discrete-time
quantum walks. For a class of walks, we show that pretty good state transfer is
characterized by the spectrum of certain Hermitian adjacency matrix of the
graph; more specifically, the vertices involved in pretty good state transfer
must be $m$-strongly cospectral relative to this matrix, and the arccosines of
its eigenvalues must satisfy some number theoretic conditions. Using normalized
adjacency matrices, cyclic covers, and the theory on linear relations between
geodetic angles, we construct several infinite families of walks that exhibits
this phenomenon.
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