Abstract
Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity–time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.
Highlights
Quantum walk [1,2,3,4,5,6] is the quantum analog of the classic random walk, which has found wide applications in many areas of quantum information science
We propose the use of a diffusion coefficient, one of the bulk properties, for characterizing the topological phases in PT-symmetric quantum walk
We proposed using the diffusion coefficient as a probe for studying the dynamics of topological edge states
Summary
Quantum walk [1,2,3,4,5,6] is the quantum analog of the classic random walk, which has found wide applications in many areas of quantum information science. First is the limited evolution time induced by dissipation and decoherence effects [22] These effects are unavoidable in open quantum walks [13,14], which is because of the non-unitary dynamics and is described in the framework of the non-Hermitian quantum mechanics [23,24]. We propose the use of a diffusion coefficient, one of the bulk properties, for characterizing the topological phases in PT-symmetric quantum walk. With this new perspective, we can address the aforementioned two issues and there is no necessity for constructing artificial boundaries.
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