Absorption Probabilities for the Two-Barrier Quantum Walk
Eric Bach, Lev Borisov · arXiv (Cornell University) · 2009
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).