Cantor correlations I. Operator systems and Cantor games
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908643120644096 |
|---|---|
| author | Baziotis, Georgios Chatzinikolaou, Alexandros Todorov, Ivan G. Turowska, Lyudmila |
| author_facet | Baziotis, Georgios Chatzinikolaou, Alexandros Todorov, Ivan G. Turowska, Lyudmila |
| contents | We study no-signalling correlations over Cantor spaces, placing the product of infinitely many copies of a finite non-local game in a unified general setup. We define the subclasses of local, quantum spatial, approximately quantum and quantum commuting Cantor correlations and describe them in terms of states on tensor products of inductive limits of operator systems. We provide a correspondence between no-signalling (resp. approximately quantum, quantum commuting) Cantor correlations and sequences of correlations of the same type over the projections onto increasing number of finitely many coordinates. We introduce Cantor games, and associate canonically such a game to a sequence of finite input/output games, showing that the numerical sequence of the values of the games in the sequence converges to the corresponding value of the compound Cantor game. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cantor correlations I. Operator systems and Cantor games Baziotis, Georgios Chatzinikolaou, Alexandros Todorov, Ivan G. Turowska, Lyudmila Operator Algebras We study no-signalling correlations over Cantor spaces, placing the product of infinitely many copies of a finite non-local game in a unified general setup. We define the subclasses of local, quantum spatial, approximately quantum and quantum commuting Cantor correlations and describe them in terms of states on tensor products of inductive limits of operator systems. We provide a correspondence between no-signalling (resp. approximately quantum, quantum commuting) Cantor correlations and sequences of correlations of the same type over the projections onto increasing number of finitely many coordinates. We introduce Cantor games, and associate canonically such a game to a sequence of finite input/output games, showing that the numerical sequence of the values of the games in the sequence converges to the corresponding value of the compound Cantor game. |
| title | Cantor correlations I. Operator systems and Cantor games |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2509.18028 |