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 of order dividing d. Such matrices appear as solutions of linear constraint systems that play a role in the study of quantum contextuality and in applications to operator-theoretic problems motivated by quantum information theory. Using methods from stable homotopy theory, we modify commutative d-torsion K-theory into a cohomology theory that can be used for studying operator solutions of linear constraint systems. This provides an interesting connection between stable homotopy theory and quantum information theory.