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arXiv · 2209.13213

Spectral mapping theorem of an abstract non-unitary quantum walk

Keisuke Asahara·Daiju Funakawa·Etsuo Segawa·Akito Suzuki·Noriaki Teranishi
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Abstract

This paper continues the previous work (Quantum Inf. Process (2019)) by two authors of the present paper about a spectral mapping property of chiral symmetric unitary operators. In physics, they treat non-unitary time-evolution operators to consider quantum walks in open systems. In this paper, we generalize the above result to include a chiral symmetric non-unitary operator whose coin operator only has two eigenvalues. As a result, the spectra of such non-unitary operators are included in the (possibly non-unit) circle and the real axis in the complex plane. We also give some examples of our abstract results, such as non-unitary quantum walks defined by Mochizuki et al. Moreover, we present an application to the Ihara zeta functions and correlated random walks on regular graphs, which are not quantum walks.

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Keisuke Asahara, Daiju Funakawa, Etsuo Segawa, Akito Suzuki, Noriaki Teranishi. 2022-09-27. Spectral mapping theorem of an abstract non-unitary quantum walk. https://arxiv.org/abs/2209.13213

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