Weak limits for quantum walks on the half-line

Abstract

For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context, localization is possible even for a walk predicated on the assumption of homogeneity. For the Hadamard walk on the half-line, the weak limit is shown to be independent of the initial coin state and to exhibit no localization.

Added references and some other updates, corrected typos

References in corpus (5)

• Universal computation by quantum walk
• Quantum walks: a comprehensive review
• Asymptotic evolution of quantum walks with random coin
• Wigner formula of rotation matrices and quantum walks
• Quantum walks and orbital states of a Weyl particle

Cited by in corpus (3)

• Two-dimensional quantum central limit theorem by quantum walks
• A quantum walk on the half line with a particular initial state
• Limit distribution of a time-dependent quantum walk on the half line