  The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is
applied to the closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological
model. We show that the phase space average for the surface of the apparent
horizon is quantized in units of the Planck's surface, and that the total
entropy of the universe is also quantized. Taking into account these two
concepts, it is shown that 't Hooft conjecture on the cosmological holographic
principle (CHP) in radiation and dust dominated quantum universes is satisfied
as a manifestation of quantization. This suggests that the entire universe (not
only inside the apparent horizon) can be seen as a two-dimensional information
structure encoded on the apparent horizon.
