  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.
