Absence of wave operators for one-dimensional quantum walks

TL;DR

This paper demonstrates that certain pairs of evolution operators in one-dimensional quantum walks lack wave operators, clarifying the boundary between short-range and long-range interactions in this quantum context.

Contribution

It establishes the non-existence of wave operators for specific pairs of evolution operators in 1D quantum walks, highlighting a key distinction in quantum walk dynamics.

Findings

Existence of pairs without wave operators in 1D quantum walks

Clarification of the boundary between short-range and long-range interactions

Implication for the classification of quantum walk behaviors

Abstract

We show that there exist pairs of two time evolution operators which do not have wave operators in a context of one-dimensional discrete time quantum walks. As a consequence, the borderline between short range type and long range type is decided.