Perfect state transfer in Grover walks on a distance-regular graph occurs exactly when the graph is antipodal with two-vertex fibres and the Chebyshev sign pattern matches the eigenvalue parity; this classifies Hamming, Johnson, and diameter-2,3 and integral distance-regular graphs.
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Perfect state transfer in Grover walks on association schemes and distance-regular graphs
Perfect state transfer in Grover walks on a distance-regular graph occurs exactly when the graph is antipodal with two-vertex fibres and the Chebyshev sign pattern matches the eigenvalue parity; this classifies Hamming, Johnson, and diameter-2,3 and integral distance-regular graphs.