Qubit and Fermionic Fock Spaces from Type II Superstring Black Holes

TL;DR

This paper establishes a correspondence between qubit and fermionic Fock spaces and extremal black holes in type II superstring theory, using complex compactifications and Hodge diagram combinatorics, revealing new insights into black hole charge structures.

Contribution

It introduces a novel mapping between qubits, fermionic spaces, and black hole charges in superstring theory, extending to Calabi-Yau manifolds and linking differential forms to quantum states.

Findings

Identifies a one-to-one correspondence between qubits, fermionic spaces, and extremal black holes.

Shows the division of qubit systems into even and odd D-brane charge sectors.

Generalizes the correspondence to Calabi-Yau compactifications.

Abstract

Using Hodge diagram combinatorial data, we study qubit and fermionic Fock spaces from the point of view of type II superstring black holes based on complex compactifications. Concretely, we establish a one-to-one correspondence between qubits, fermionic spaces and extremal black holes in maximally supersymmetric supergravity obtained from type II superstring on complex toroidal and Calabi-Yau compactifications. We interpret the differential forms of the n-dimensional complex toroidal compactification as states of n-qubits encoding information on extremal black hole charges. We show that there are 2^n copies of n-qubit systems which can be split as 2^n=2^{n-1}+2^{n-1}. More precisely, 2^{n-1} copies are associated with even D-brane charges in type IIA superstring and the other 2^{n-1} ones correspond to odd D-brane charges in IIB superstring. This correspondence is generalized to a class of Calabi-Yau manifolds. In connection with black hole charges in type IIA superstring, an n-qubit system has been obtained from a canonical line bundle of n factors of one dimensional projective space \mathbb{CP}^1.