Magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy

Abstract

Abstract:We investigate the structure of the three-qubit magic Veldkamp line (MVL). This mathematical notion has recently shown up as a tool for understanding the structures of the set of Mermin pentagrams, objects that are used to rule out certain classes of hidden variable theories. Here we show that this object also provides a unifying finite geometric underpinning for understanding the structure of functionals used in form theories of gravity and black hole entropy. We clarify the representation theoretic, finite geometric and physical meaning of the different parts of our MVL. The upshot of our considerations is that the basic finite geometric objects enabling such a diversity of physical applications of the MVL are the unique generalized quadrangles with lines of size three, their one point extensions as well as their other extensions isomorphic to affine polar spaces of rank three and order two. In a previous work we have already connected generalized quadrangles to the structure of cubic Jordan algebras related to entropy fomulas of black holes and strings in five dimensions. In some respect the present paper can be regarded as a generalization of that analysis for also providing a finite geometric understanding of four -dimensional black hole entropy formulas. However, we find many more structures whose physical meaning is yet to be explored. As a familiar special case our work provides a finite geometric representation of the algebraic extension from cubic Jordan algebras to Freudenthal systems based on such algebras.

Four-qubit systems and dyonic black Hole–Black branes in superstring theory

“…SO (4)×SO (20) represents the geometric deformations of the K3 surface in the presence of the antisymmetric B-field of the NS-NS sector and it is linked to the symmetry group G 1 = U (1) 24 . However, the second factor SO(1, 1) represents the dilaton scalar field which is associated with G 2 = U (1) [35,36].…”

“…The black objects, embedded in superstring theory compactifications, can be connected to quantum information theory using the qubit analysis [12][13][14][15][16][17][18][19][20][21][22][23][24]. Precisely, a fascinating correspondence has been discovered between quantum information theory and superstring theory.…”

Stringy dyonic solutions and clifford structures

“…Considering Dbrane physics, several compactfications producing some black brane solutions embedded in type II superstrings have been studied [6,7,8]. It has been shown that these black objects can be linked to many subjects including quantum information theory by exploiting the qubit mathematical formalism [9,10,11,12,13,14,15,16]. Concretely, a remarkable correspondence between qubit systems and black holes in superstring theory has been established.…”

A Combinatorial Grassmannian Representation of the Magic Three-Qubit Veldkamp Line

“…One of the most startling results of the finite-geometric approach to the field of quantum information and the so-called black-hole/qubit correspondence is undoubtedly the recent discovery [1,2] of the existence of a magic Veldkamp line associated with the five-dimensional binary symplectic polar space W (5, 2) ( the finite-geometrical concepts, symbols, and notation are explained in the next section) underlying the geometry of the three-qubit Pauli group. There are as many as five different types of Veldkamp lines in W (5, 2) [3] (see also [4] for a detailed discussion of the Veldkamp space of W (3, 2)).…”