Qubit and fermionic Fock spaces from type II superstring black holes

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 [Formula: see text]-dimensional complex toroidal compactification as states of [Formula: see text]-qubits encoding information on extremal black hole charges. We show that there are [Formula: see text] copies of [Formula: see text] qubit systems which can be split as [Formula: see text]. More precisely, [Formula: see text] copies are associated with even [Formula: see text]-brane charges in type IIA superstring and the other [Formula: see text] ones correspond to odd [Formula: see text]-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 [Formula: see text]-qubit system has been obtained from a canonical line bundle of [Formula: see text] factors of one-dimensional projective space [Formula: see text]