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 nn-dimensional complex toroidal compactification as states of nn-qubits encoding information on extremal black hole charges. We show that there are 2n2n copies of nn qubit systems which can be split as 2n=2n−1+2n−12n=2n−1+2n−1. More precisely, 2n−12n−1 copies are associated with even DD-brane charges in type IIA superstring and the other 2n−12n−1 ones correspond to odd DD-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 nn-qubit system has been obtained from a canonical line bundle of nn factors of one-dimensional projective space ℂℙ1.
