  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 which can be used for studying operator solutions of linear constraint
systems. This provides an interesting connection between stable homotopy theory
and quantum information theory.
