Cantor correlations I. Operator systems and Cantor games
Preprint, 2025

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.

Författare

Alexandros Chatzinikolaou

George Baziotis

Lyudmyla Turowska

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Icke-kommutativanalys för kvantberäkningar

Vetenskapsrådet (VR) (2023-04555), 2024-01-01 -- 2027-12-31.

Fundament

Grundläggande vetenskaper

Ämneskategorier (SSIF 2025)

Matematisk analys

DOI

10.48550/arXiv.2509.18028

Mer information

Senast uppdaterat

2026-01-30