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Quantum fractional revival on graphs. (English) Zbl 1441.05134
Summary: Fractional revival is a quantum transport phenomenon important for entanglement generation in spin networks. This takes place whenever a continuous-time quantum walk maps the characteristic vector of a vertex to a superposition of the characteristic vectors of a subset of vertices containing the initial vertex. A main focus will be on the case when the subset has two vertices. We explore necessary and sufficient spectral conditions for graphs to exhibit fractional revival. This provides a characterization of fractional revival in paths and cycles. Our work builds upon the algebraic machinery developed for related quantum transport phenomena such as state transfer and mixing, and it reveals a fundamental connection between them.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C72 Fractional graph theory, fuzzy graph theory
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
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