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 SO(4,4) SO(4)×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.

Stringy dyonic solutions and clifford structures

“…In this section, we reconsider the study of dyonic solutions in type II superstrings compactified on n-dimensional real manifolds X n . It has been remarked that each compact manifold possesses some geometric information which can play a crucial role in the determination of the superstring theory spectrum in 10 − n dimensions [22]. In particular, they can be exploited to produce all physical data in lower dimensional superstring models.…”

“…Using string dualities between type IIA and heterotic superstrings, four-qubit systems in the context of type II superstring compactifications have been investigated [20,21]. It has been revealed that such qubit systems are related to a stringy moduli space SO(4,4) SO(4)×SO(4) considered as a reduction of the moduli space of six dimensional supergravity model obtained from the compactification of the heterotic superstring on T 4 [22]. Moreover, the string/string duality has been exploited to show that there exists an interplay between four-qubit states and a particular ordinary dyonic black hole in six dimensions having eight electric and eight magnetic charges.…”

Entanglement and non-locality of four-qubit connected hypergraph states

“…Since then the four-qubit classification has generated a large amount of work including alternative perspectives on the classification itself [26,10,24,22,8], invariants-covariants approches of the classification [25,33,27], geometric intepretations [23,20,21,26] and connection with others domains in physics [5,6,4]. Hypergraph states are quantum states that generalize the notion of graph states where qubits composing the system are given by vertices and the interaction between the qubits/vertices are described by edges or hyperedges (See Sec.…”

Geometric engineering of qubits from string theory

“…Among others, works based on toric manifolds has been developed leading to a classification of qubit systems in terms of black hole charges in type II superstrings in the presence of D-brane objects [16]. Moreover, some studies have been proposed by using the Andinkra graph theory being exploited in the study of the supersymmetric representation theory [13,14,15,16,17]. In particular, these graphs have been elaborated to classify a class of qubits linked to extremal black branes in type II superstring compactified on complex manifolds [13].…”