Quantum Holography from Fermion Fields

TL;DR

This paper demonstrates how fermion fields in Loop Quantum Gravity encode qubits on boundary surfaces, supporting the Quantum Holographic Principle through a novel fermionic and geometric framework.

Contribution

It introduces fermion fields and Bogoljubov transformations in Loop Quantum Gravity to encode qubits on boundary surfaces, extending the holographic principle.

Findings

Boundary surface encodes a qubit per Planck area unit.

Doubling fermionic degrees of freedom leads to pixelation of area.

Proof extends to fuzzy sphere geometries.

Abstract

We demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogoljubov transformations lead to pairs of spin network's edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.