A one-dimensional Hadamard walk with one defect

Abstract

We consider a one-dimensional space-inhomogeneous discrete time quantum walk. This model is the Hadamard walk with one defect at the origin which is different from the model introduced by Wojcik et al. [14]. We obtain a stationary measure of the model by solving the eigenvalue problem and an asymptotic behaviour of the return probability by the path counting approach. Moreover, we get the time-averaged limit measure using the space-time generating function method. The measure is symmetric for the origin and independent of the initial coin state at the starting point. So localization depends only on the parameter which determines the model.

32 pages

References in corpus (2)

• The stationary measure of a space-inhomogeneous quantum walk on the line
• The time-averaged limit measure of the Wojcik model

Cited by in corpus (7)

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• Eigenvalues of two-phase quantum walks with one defect in one dimension
• Stationary measures for the three-state Grover walk with one defect in one dimension
• Weak limit theorem of a two-phase quantum walk with one defect
• Strongly trapped space-inhomogeneous quantum walks in one dimension
• The stationary measure for diagonal quantum walk with one defect
• Stationary measure for three-state quantum walk