Secret communication games and a hierarchy of quasiparticle statistics in 3 + 1D topological phases
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917066757373952 |
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| author | Wang, Zhiyuan |
| author_facet | Wang, Zhiyuan |
| contents | We show that a family of secret communication challenge games naturally define a hierarchy of emergent quasiparticle statistics in three-dimensional (3D) topological phases. The winning strategies exploit a special class of the recently proposed $R$-paraparticles to allow nonlocal secret communication between the two participating players. We first give a high-level, axiomatic description of emergent $R$-paraparticles, and show that any physical system hosting such particles admits a winning strategy. We then analyze the games using the categorical description of topological phases (where point-like excitations in 3D are described by symmetric fusion categories), and show that only $R$-paraparticles can win the 3D challenge in a noise-robust way, and the winning strategy is essentially unique. This analysis associates emergent $R$-paraparticles to deconfined gauge theories based on an exotic class of finite groups. Thus, even though this special class of $R$-paraparticles are fermions or bosons under the categorical classification, their exchange statistics can still have nontrivial physical consequences in the presence of appropriate defects, and the $R$-paraparticle language offers a more convenient description of the winning strategies. Finally, while a subclass of non-Abelian anyons can win the game in 2D, we introduce twisted variants that exclude anyons, thereby singling out $R$-paraparticles in 2D as well. Our results establish the secret communication challenge as a versatile diagnostic for both identifying and classifying exotic exchange statistics in topological quantum matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Secret communication games and a hierarchy of quasiparticle statistics in 3 + 1D topological phases Wang, Zhiyuan Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics We show that a family of secret communication challenge games naturally define a hierarchy of emergent quasiparticle statistics in three-dimensional (3D) topological phases. The winning strategies exploit a special class of the recently proposed $R$-paraparticles to allow nonlocal secret communication between the two participating players. We first give a high-level, axiomatic description of emergent $R$-paraparticles, and show that any physical system hosting such particles admits a winning strategy. We then analyze the games using the categorical description of topological phases (where point-like excitations in 3D are described by symmetric fusion categories), and show that only $R$-paraparticles can win the 3D challenge in a noise-robust way, and the winning strategy is essentially unique. This analysis associates emergent $R$-paraparticles to deconfined gauge theories based on an exotic class of finite groups. Thus, even though this special class of $R$-paraparticles are fermions or bosons under the categorical classification, their exchange statistics can still have nontrivial physical consequences in the presence of appropriate defects, and the $R$-paraparticle language offers a more convenient description of the winning strategies. Finally, while a subclass of non-Abelian anyons can win the game in 2D, we introduce twisted variants that exclude anyons, thereby singling out $R$-paraparticles in 2D as well. Our results establish the secret communication challenge as a versatile diagnostic for both identifying and classifying exotic exchange statistics in topological quantum matter. |
| title | Secret communication games and a hierarchy of quasiparticle statistics in 3 + 1D topological phases |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2510.11818 |