Graph theory and qubit information systems of extremal black branes

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.

Toric geometry and string theory descriptions of qudit systems

“…n qubits, in fact, are 2 n configuration states which can be represented by graphs sharing a strong resemblance with a particular class of Adinkras formed by 2 n nodes connected with n colored lines [11]. This observation has been explored to show a new similarity between n qubit systems and 2 n cycles embedded in n-dimensional torii T n .…”

“…It is shown that the quantum bit or the qubit, which is based on a superposition of the two possible states, is considered as the most basic building block of such quantum theories. In fact, qubit and its generalizations are connected to many theories including string theory, D-branes, black holes, toric geometry and supermanifolds [7,8,9,10,11]. A particular emphasis put on the link with the black holes and branes obtained from supergravity models in high dimensions.…”

Stringy dyonic solutions and clifford structures

“…Concretely, a remarkable correspondence between qubit systems and black holes in superstring theory has been established. The relevant findings concern a nice link between the N = 2 STU black hole with eight charges and threequbit system states [13,17,18,19]. The analysis has been developed to describe structures going beyond such extremal black hole solutions in terms of higher dimensional qubit systems.…”

Four-qubit systems and dyonic black Hole–Black branes in superstring theory

“…The main obtained relations are between the entropy formulas for specific black hole solutions in supergravity theories and entanglement measures for certain multiqubit systems [17,18]. Alternative studies have been conducted using toric geometry and graph theory [24,25,26,27].…”