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arXiv · 1805.11742

Detection of edge defects by embedded eigenvalues of quantum walks

Hisashi Morioka·Etsuo Segawa
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Abstract

We consider a position-dependent quantum walk on ${\bf Z}$. In particular, we derive a detection method for edge defects by embedded eigenvalues of its time evolution operator. In the present paper, the set of edge defects is that of points in ${\bf Z}$ on which the coin operator is an anti-diagonal matrix. In fact, under some suitable assumptions, the existence of a finite number of edge defects is equivalent to the existence of embedded eigenvalues of the time evolution operator.

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Hisashi Morioka, Etsuo Segawa. 2019-08-01. Detection of edge defects by embedded eigenvalues of quantum walks. https://doi.org/10.1007/s11128-019-2398-z

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