Hitchin functionals are related to measures of entanglement

TL;DR

This paper reveals a deep connection between Hitchin functionals in form theories of gravity and measures of quantum entanglement, unifying concepts from supergravity, topological strings, and quantum information.

Contribution

It establishes a novel link between Hitchin functionals and entanglement measures, introducing the use of Hitchin invariants as tools for classifying multipartite entanglement.

Findings

Hitchin functionals relate to entanglement measures in quantum systems.

Freudenthal duality connects nonlinear functionals to entanglement classification.

Hitchin invariants can classify three-fermion systems with seven modes.

Abstract

According to the Black Hole/Qubit Correspondence (BHQC) certain black hole entropy formulas in supergravity can be related to multipartite entanglement measures of quantum information. Here we show that the origin of this correspondence is a connection between Hitchin functionals used as action functionals for form theories of gravity related to topological strings, and entanglement measures for systems with a small number of constituents. The basic idea acting as a unifying agent in these seemingly unrelated fields is stability connected to the mathematical notion of special prehomogeneous vector spaces associated to Freudenthal systems coming from simple Jordan algebras. It is shown that the nonlinear function featuring these functionals and defining Calabi-Yau and generalized Calabi-Yau structures is the Freudenthal dual a concept introduced recently in connection with the BHQC. We propose to use the Hitchin invariant for three-forms in 7 dimensions as an entanglement measure playing a basic role in classifying three-fermion systems with seven modes. The representative of the class of maximal tripartite entanglement is the three-form used as a calibration for compactification on manifolds with $G_2$ holonomy. The idea that entanglement measures are related to action functionals from which the usual correspondence of the BHQC follows at the tree level suggests that one can use the BHQC in a more general context.