Four-qubit Systems and Dyonic Black Hole-Black Branes in Superstring Theory

Abstract

Using dyonic solutions in the type IIA superstring theory on Calabi-Yau manifolds, we reconsider the study of black objects and quantum information theory using string/string duality in six dimensions. Concretely, we relate four-qubits with a stringy quaternionic moduli space of type IIA compactification associated with a dyonic black solution formed by black holes (BH) and black 2-branes (B2B) carrying 8 electric charges and 8 magnetic charges. This connection is made by associating the cohomology classes of the heterotic superstring on T^{4} to four-qubit states. These states are interpreted in terms of such dyonic charges resulting from the quaternionic symmetric space \frac{SO(4,4)}{SO(4)\times SO(4)} corresponding to a N=4 sigma model superpotential in two dimensions. The superpotential is considered as a functional depending on four quaternionic fields mapped to a class of Clifford algebras denoted as Cl_{0,4}. A link between such an algebra and the cohomology classes of T^4 in heterotic superstring theory is also given.