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arXiv · 2610.26204

Wave-Particle Complementarity in Quantum Walk from a Quantum Mechanical Perspective

Norio Konno·Shigeki Matsutani·Etsuo Segawa·Tomoyuki Terada
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Abstract

A quantum walk is a mathematical model and a quantum version of a random walk. For the past two decades, it has been studied from mathematical and physical viewpoints. It has many desirable properties. This paper reevaluates quantum walk from a quantum mechanical perspective, as Feynman essentially proposed it as a toy model in his path integral method. Then we demonstrate that the quantum walk model exhibits both particle-like and wave-like properties by showing reflection and partial reflection as a particle and interference as a wave. In particular, for an initial state supported at two sites $\pm\ell$, we explicitly derive the weak limit distribution of the Hadamard walk and show that the Konno distribution is modulated by the interference factor $2\cos^2(\ell k(x))$. The resulting interference profile is reminiscent of far-field (Fraunhofer-type) diffraction.

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Norio Konno, Shigeki Matsutani, Etsuo Segawa, Tomoyuki Terada. 2026-10-19. Wave-Particle Complementarity in Quantum Walk from a Quantum Mechanical Perspective. https://arxiv.org/abs/2610.26204

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