Absorption problems for quantum walks in one dimension

Abstract

This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N is finite or infinite by using a new path integral approach based on an orthonormal basis P, Q, R and S of the vector space of complex 2 times 2 matrices. Our method studied here is a natural extension of the approach in the classical random walk.

15 pages, small corrections, journal reference added

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