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PreprintCC BY 4.0arXiv

Entanglement entropy in two-particle Grover walks on graphs

  • Sho Kubota
  • Haruhiko Matsubara
  • Etsuo Segawa
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Abstract

We define a two-particle quantum walk of identical particles on a graph G via the one-particle Grover walk on the Kronecker product G ⊗ G, and call it the two-particle Grover walk. In systems of identical particles, quantum mechanics requires that quantum states have a certain invariance with respect to the exchange of particles. Focusing on the symmetry of the Kronecker product G ⊗ G as a graph, we show that the time evolution operator of this walk commutes with the swap operator, which ensures that this requirement is satisfied. Furthermore, we study the entanglement entropy of quantum states evolved by this walk. For the complete bipartite graph Kn,n, we completely determine the values of n for which the quantum states evolved from specific initial states attain the upper bound of the entropy at some time, and prove that they are exactly $1$ and $2$.

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Cite

BibTeXRIS
BibTeX
@misc{kubota2026entanglement,
  title = {{Entanglement entropy in two-particle Grover walks on graphs}},
  author = {Sho Kubota and Haruhiko Matsubara and Etsuo Segawa},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.09066},
  eprint = {2607.09066},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.09066},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Entanglement entropy in two-particle Grover walks on graphs
AU  - Sho Kubota
AU  - Haruhiko Matsubara
AU  - Etsuo Segawa
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2607.09066
UR  - https://arxiv.org/abs/2607.09066
AB  - We define a two-particle quantum walk of identical particles on a graph G via the one-particle Grover walk on the Kronecker product G ⊗ G, and call it the two-particle Grover walk. In systems of identical particles, quantum mechanics requires that quantum states have a certain invariance with respect to the exchange of particles. Focusing on the symmetry of the Kronecker product G ⊗ G as a graph, we show that the time evolution operator of this walk commutes with the swap operator, which ensures that this requirement is satisfied. Furthermore, we study the entanglement entropy of quantum states evolved by this walk. For the complete bipartite graph K_n,n, we completely determine the values of n for which the quantum states evolved from specific initial states attain the upper bound of the entropy at some time, and prove that they are exactly $1$ and $2$.
ER  -