Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 5 min ago
PreprintarXiv licencearXiv

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

  • Norio Konno
  • Shigeki Matsutani
  • Etsuo Segawa
  • Tomoyuki Terada
Open at sourcePDFDOICite

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 ±ℓ, we explicitly derive the weak limit distribution of the Hadamard walk and show that the Konno distribution is modulated by the interference factor 2cos2(ℓ k(x)). The resulting interference profile is reminiscent of far-field (Fraunhofer-type) diffraction.

Related

  1. An implicit multiscale solver for steady kinetic equations based on wave-particle decomposition
    Chang Liu, Kun Xu
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingComputational physicsarXiv
  2. Wave-Particle Decomposition for Kinetic Equations II: Full Boltzmann equation
    Chang Liu, Kun Xu
    arXivPreprintCC BY 4.0Full textMathematical physicsFluid dynamicsarXiv
  3. Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice
    Mashrab Akramov, Carsten Trunk, Davron Matrasulov
    arXivPreprintCC BY 4.0Full textMathematical physicsQuantum physics & quantum informationarXiv
  4. Optimal Control for Cancer Chemotherapy Using Hybrid Quantum Particle Swarm Optimization
    Bereket Sitotaw Kidane, Md Samiul Haque Motayed, Shuo Wang
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  5. Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction
    Taehee Ko, Sungbin Lim, Sangkook Choi
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingQuantum physics & quantum informationarXiv

Cite

BibTeXRIS
BibTeX
@misc{konno2026waveparticle,
  title = {{Wave-Particle Complementarity in Quantum Walk from a Quantum Mechanical Perspective}},
  author = {Norio Konno and Shigeki Matsutani and Etsuo Segawa and Tomoyuki Terada},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26204},
  eprint = {2610.26204},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26204},
}
RIS
TY  - UNPB
TI  - Wave-Particle Complementarity in Quantum Walk from a Quantum Mechanical Perspective
AU  - Norio Konno
AU  - Shigeki Matsutani
AU  - Etsuo Segawa
AU  - Tomoyuki Terada
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26204
UR  - https://arxiv.org/abs/2610.26204
AB  - 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 ±ℓ, we explicitly derive the weak limit distribution of the Hadamard walk and show that the Konno distribution is modulated by the interference factor 2cos^2(ℓ k(x)). The resulting interference profile is reminiscent of far-field (Fraunhofer-type) diffraction.
ER  -