Josse van Dobben de Bruyn: [WS1] Mermin–Peres magic rectangles modulo odd primes

Speaker
Josse van Dobben de Bruyn, Charles University, Prague

Abstract
The Mermin–Peres square and similar examples show that a linear system over ℤ/2ℤ with no classical solutions can have an operator solution, paving the way for the rich theory of linear constraint system (LCS) games. LCS games over ℤ/2ℤ are quite well understood and have been used to prove deep results in QIT, including undecidability in nonlocal games and separations between correlation sets. By contrast, LCS games over ℤ/dℤ with d odd remain poorly understood, and no Mermin–Peres-like (finite-dimensional) pseudotelepathy scenarios are known in this setting. This problem has received considerable attention from researchers in nonlocal games, noncommutative constraint satisfaction problems, and contextuality, and it was recently conjectured by Chung, Okay and Sikora that no such examples exist. In this talk, I will use graph theory to explain why it is harder to get pseudotelepathy modulo odd numbers, and I will present the first known examples of Mermin–Peres-like magic rectangles with finite-dimensional operators of odd prime order. This talk is based on joint work with David Roberson and runs parallel to recent work of Slofstra and Zhang, who found the first such examples in the commuting operator model.