Quantum / CONCEPT

No perfect state transfer at time pi on rational paths with 2^k + 1 vertices

Kirkland, McLaren, Pereira, Plosker and Zhang (arXiv:1708.03283) conjecture that a weighted path on at least four vertices, with or without potentials, whose edge weights are all rational has no perfect state transfer between its end vertices at readout time pi, and prove it for n = 4 and for n congruent to 3 or 5 modulo 8. For every k >= 1 the statement holds for the paths on n = 2^k + 1 vertices, with arbitrary real potentials and in both directions; for k >= 3 these sizes are congruent to 1 modulo 8.