Speaker
Lyudmila Turowska, Chalmers University of Technology and University of Gothenburg
Abstract
Parallel repetition plays a central role in the study of asymptotic values of non-local games and in distinguishing classical from quantum models, with important applications to device-independent cryptography. Countable parallel repetition naturally leads to games over Cantor spaces, where inputs and outputs are infinite strings and successive rounds need not be independent or identical. This provides a flexible framework for studying non-local games with memory and infinite outcome sets. In this talk, I will introduce no-signalling Cantor correlations as strategies for Cantor games, focusing on bisynchronous graded correlations. While finite bisynchronous correlations are characterized by traces on quantum permutation groups, their Cantor counterparts are connected to infinite free wreath products of quantum permutation groups and to factorizable maps on infinite-dimensional spaces with prescribed ancillas. I will also discuss isomorphism of Cantor graphs from an operational perspective and explain its relation to quantum isomorphism of certain locally finite level graphs in the sense of Rollier and Vaes.
Lyudmila Turowska, Chalmers University of Technology and University of Gothenburg
Abstract
Parallel repetition plays a central role in the study of asymptotic values of non-local games and in distinguishing classical from quantum models, with important applications to device-independent cryptography. Countable parallel repetition naturally leads to games over Cantor spaces, where inputs and outputs are infinite strings and successive rounds need not be independent or identical. This provides a flexible framework for studying non-local games with memory and infinite outcome sets. In this talk, I will introduce no-signalling Cantor correlations as strategies for Cantor games, focusing on bisynchronous graded correlations. While finite bisynchronous correlations are characterized by traces on quantum permutation groups, their Cantor counterparts are connected to infinite free wreath products of quantum permutation groups and to factorizable maps on infinite-dimensional spaces with prescribed ancillas. I will also discuss isomorphism of Cantor graphs from an operational perspective and explain its relation to quantum isomorphism of certain locally finite level graphs in the sense of Rollier and Vaes.