Hitchin functionals are related to measures of entanglement

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.

55 pages, Latex

References in corpus (22)

• Hidden Variables and the Two Theorems of John Bell
• Generalised Geometry for M-Theory
• General criterion for the entanglement of two indistinguishable particles
• Four-qubit entanglement from string theory
• Black Holes, Qubits and Octonions
• Strings, Black Holes, and Quantum Information
• Black holes admitting a Freudenthal dual
• The black-hole/qubit correspondence: an up-to-date review
• Stringy Black Holes and the Geometry of Entanglement
• E_7 and the tripartite entanglement of seven qubits
• Pairing in fermionic systems: A quantum information perspective
• Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes
• Three fermions with six single particle states can be entangled in two inequivalent ways
• Non-supersymmetric Black Holes and Topological Strings
• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• On the Black-Hole/Qubit Correspondence
• E_6 and the bipartite entanglement of three qutrits
• Attractors with Vanishing Central Charge
• Wrapped branes as qubits
• Black Hole Entropy and Finite Geometry
• A three-qubit interpretation of BPS and non-BPS STU black holes
• STU attractors from vanishing concurrence

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• Freudenthal Dual Lagrangians
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• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
• Black holes and general Freudenthal transformations
• Toric Geometry and String Theory Descriptions of Qudit Systems
• Black hole qubit correspondence from quantum circuits
• Classification of multipartite systems featuring only $|W⟩$ and $|GHZ⟩$ genuine entangled states
• Qubits from Adinkra Graph Theory via Colored Toric Geometry
• Freudenthal ranks: GHZ vs. W