Absorption Probabilities for the Two-Barrier Quantum Walk

Eric Bach; Lev Borisov

arxiv: 0901.4349 · v1 · submitted 2009-01-27 · 🪐 quant-ph · math.NT

Absorption Probabilities for the Two-Barrier Quantum Walk

Eric Bach , Lev Borisov This is my paper

classification 🪐 quant-ph math.NT

keywords formulaquantumwalkabsorbedabsorptionconcerningconjectureempirically

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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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