Absorption Probabilities for the Two-Barrier Quantum Walk

Details Absorption Probabilities for the Two-Barrier Quantum Walk Absorption Probabilities for the Two-Barrier Quantum Walk

2009-01-27

arxiv.org/abs/0901.4349v1

Physics

Quantum Physics

11 pages

Scientific paper

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).

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