[carlosjobim]

If we assume that digital video/film recording will compress the spectrum to images which are composed of three colors, somewhere in the processes between the light hitting the camera and the light being emitted from a display to the viewer, that means any tetrachromatic person will notice a difference between the images and the real world.

[glkindlmann]

Sure, but noticing a difference between the images and the real world also happens with us trichromats too, e.g. colors online don't match those in the real world if the illuminant isn't correctly controlled. The intrinsic difficulty of color reproduction is not the same as detecting tetrachromacy. The nuance here is in generating stimuli that reliably and specifically detect the difference between projecting from an infinite-D space of spectra down to 3D (via metamers like the "keef" and "litz" described in the paper linked above), versus projecting down to 4D.

[carlosjobim]

The difference between display and real world will be at most slight to a trichromat, while it would be extraordinarily obvious to a tetrachromat.

It's not very uncommon for people to be colour blind, dichromats. If media on screens would be dichromatic while the world around me is trichromatic, I would certainly notice at once.

[glkindlmann]

I suggest trying to quantify "extraordinarily", using the actual spectral response curve for the tetrachromat's fourth cone, called "Q" in the paper shared by varunneal. Most people casually equate the short (S), medium (M), and long (L) cones with blue, green, and red, with the idea that these are all as different as can be, but the M and L cones are very similar to each other, compared to S. The L, M, S curves are independent but far from orthogonal in the way you may be thinking as you say "extraordinarily". The Q curve is just another wide bump, with a peak in between that of M and L, so again, very far from being orthogonal. Whatever 4th dimension of color perception is accessed by the Q curve, it is a relatively cramped dimension, so reliably detecting perception along it requires some carefully designed stimuli.