Localization of space-inhomogeneous three-state quantum walks

Abstract

Mathematical analysis on the existence of eigenvalues is essential because it is equivalent to the occurrence of localization, which is an exceptionally crucial property of quantum walks. We construct the method for the eigenvalue problem via the transfer matrix for space-inhomogeneous $n$-state quantum walks in one dimension with $n-2$ self-loops, which is an extension of the technique in a previous study (Quantum Inf. Process 20(5), 2021). This method reveals the necessary and sufficient condition for the eigenvalue problem of a two-phase three-state quantum walk with one defect whose time evolution varies in the negative part, positive part, and at the origin.

13 pages, 8 figures

References in corpus (8)

• Topological characterization of periodically-driven quantum systems
• Spatial search by quantum walk
• Weak Limit of the 3-State Quantum Walk on the Line
• Limit distributions of three-state quantum walks: the role of coin eigenstates
• Fully spin-polarized nodal chain state in half metal LiV${}_2$O${}_4$
• Eigenvalues of two-phase quantum walks with one defect in one dimension
• Coins Make Quantum Walks Faster
• A new type of quantum walks based on decomposing quantum states

Cited by in corpus (2)

• Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk
• Spectral analysis of three-state quantum walks with general coin matrices