Quantum nonlocal games and the d-torsion commutative space

Abstract: Nonlocal games have played a prominent role in quantum information theory by demonstrating the power of non-locality. In particular, the 'magic' examples due to Mermin and Peres belong to the class of linear system games. The Mermin-Peres games have no classical solutions, but they admit operator solutions.

In this talk, we translate the problem of finding operator solutions into a problem of extensions for partial groups (in the sense of Broto-Gonzalez). In particular, we define the d-torsion commutative nerve for groups, whose homotopy structure is crucial to identify a practical criterion (in terms of higher limits) to test a conjecture due to Chung-Okay-Sikora regarding linear system games over Z_d, with d odd.

This is joint work with Ho Yiu Chung and Cihan Okay.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos