Quantum / CONCEPT

No perfect state transfer at time pi on rational paths with an odd number of 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. The statement holds for every odd number of vertices n = 2m + 1 with m >= 1, with arbitrary real potentials and in both directions. The even sizes n = 2m with m congruent to 2 modulo 4 or to 3 or 5 modulo 8 are settled in D5/S3/Quantum/Dynamics/EvenPathRationalWeightTransfer; the conjecture remains open for n congruent to 0 modulo 8 and for n congruent to 2 or 14 modulo 16.