Pretty good state transfer in Grover walks on abelian Cayley graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911103673434112 |
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| author | Bhakta, Koushik Bhattacharjya, Bikash |
| author_facet | Bhakta, Koushik Bhattacharjya, Bikash |
| contents | In this paper, we study pretty good state transfer (PGST) in Grover walks on graphs. We consider transfer of quantum states that are localized at the vertices of a graph and we use Chebyshev polynomials to analyze PGST between such states. In general, we find a necessary and sufficient condition for the occurrence of PGST on graphs. We then focus our analysis on abelian Cayley graphs and derive a necessary and sufficient condition for the occurrence of PGST on such graphs. Consequently, we obtain a complete characterization of PGST on unitary Cayley graphs. Our results yield infinite families of graphs that exhibit PGST but fail to exhibit perfect state transfer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pretty good state transfer in Grover walks on abelian Cayley graphs Bhakta, Koushik Bhattacharjya, Bikash Combinatorics Quantum Physics 05C50, 81Q99 In this paper, we study pretty good state transfer (PGST) in Grover walks on graphs. We consider transfer of quantum states that are localized at the vertices of a graph and we use Chebyshev polynomials to analyze PGST between such states. In general, we find a necessary and sufficient condition for the occurrence of PGST on graphs. We then focus our analysis on abelian Cayley graphs and derive a necessary and sufficient condition for the occurrence of PGST on such graphs. Consequently, we obtain a complete characterization of PGST on unitary Cayley graphs. Our results yield infinite families of graphs that exhibit PGST but fail to exhibit perfect state transfer. |
| title | Pretty good state transfer in Grover walks on abelian Cayley graphs |
| topic | Combinatorics Quantum Physics 05C50, 81Q99 |
| url | https://arxiv.org/abs/2508.09711 |