English

Absorption Probabilities for the Two-Barrier Quantum Walk

Quantum Physics 2010-07-16 v1 Number Theory

Abstract

Let p_j^(n) be the probability that a Hadamard quantum walk, started at site j on the integer lattice {0,...,n}, is absorbed at 0. We give an explicit formula for p_j^(n). Our formula proves a conjecture of John Watrous, concerning an empirically observed linear fractional recurrence relation for the numbers p_1^(n).

Cite

@article{arxiv.0901.4349,
  title  = {Absorption Probabilities for the Two-Barrier Quantum Walk},
  author = {Eric Bach and Lev Borisov},
  journal= {arXiv preprint arXiv:0901.4349},
  year   = {2010}
}

Comments

11 pages

R2 v1 2026-06-21T12:05:19.071Z