Commutative d-Torsion K-Theory and Its Applications

Abstract

Commutative d-torsion K-theory is a variant of topological K-theory constructed from commuting unitary matrices whose order divides d. Such matrices appear as solutions of linear constraint systems that play a role in quantum contextuality and non-local games. Using methods from stable homotopy theory we modify commutative d-torsion K-theory into a cohomology theory which can be used for studying operator solutions of linear constraint systems. This provides an interesting connection between stable homotopy theory and operator theoretic problems motivated by quantum information theory.