Commutative d-Torsion K-Theory and Its Applications

TL;DR

This paper introduces a new cohomology theory based on commutative d-torsion K-theory, linking stable homotopy theory with quantum information applications involving linear constraint systems and quantum contextuality.

Contribution

It develops a modified cohomology theory from commutative d-torsion K-theory using stable homotopy methods, enabling new analysis of operator solutions in quantum information.

Findings

Connects stable homotopy theory with quantum contextuality.

Provides a new mathematical framework for studying linear constraint systems.

Enables analysis of operator solutions in quantum information theory.

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 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.