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Localization of Multi-State Quantum Walk in One Dimension

Norio Inui·Norio Konno
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Abstract

We show analytically that particle trapping appears in a quantum process called "quantum walk", in which the particle moves macroscopically correlating to the inner states. It has been well known that a particle in the ``Hadamard walk" with two inner states spreads away quickly on a line. In contrast, we find one-dimensional quantum walk with multi-state in which a particle stays at the starting point entirely with high positive probability. This striking difference is explained from difference between degeneration of eigenvalues of the time-evolution matrices.

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Norio Inui, Norio Konno. 2005-03-01. Localization of Multi-State Quantum Walk in One Dimension. https://doi.org/10.1016/j.physa.2004.12.060

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