Graph Theory and Qubit Information Systems of Extremal Black Branes

TL;DR

This paper explores a novel connection between graph theory, quantum information, and extremal black branes, using Adinkras to represent qubit systems and their relation to superstring compactifications.

Contribution

It establishes a one-to-one correspondence between qubit systems, Adinkras, and extremal black branes in type IIA superstring theory, extending to superqubits and supermanifolds.

Findings

Derived general expressions for bosonic and fermionic state counts.

Mapped qubit states to geometric Adinkra structures.

Linked black brane charges to qubit configurations.

Abstract

Using graph theory based on Adinkras, we consider once again the study of extremal black branes in the framework of quantum information. More precisely, we propose a one to one correspondence between qubit systems, Adinkras and certain extremal black branes obtained from type IIA superstring compactified on T^n. We accordingly interpret the real Hodge diagram of T^n as the geometry of a class of Adinkras formed by 2^n bosonic nodes representing n qubits. In this graphic representation, each node encodes information on the qubit quantum states and the charges of the extremal black branes built on T^n. The correspondence is generalized to n superqubits associated with odd and even geometries on the real supermanifold T^{n|n}. Using a combinatorial computation, general expressions describing the number of the bosonic and the fermionic states are obtained.