1) Despite the authors' terminology, the paper on PEPS is not talking about the holographic principle. The holographic principle is about an equivalence between a higher-dimensional theory and a lower-dimensional theory, but their mapping is not an equivalence. You cannot reconstruct the whole of the bulk theory from their boundary theory (see the remark on page 3 about their mapping not being http://en.wikipedia.org/wiki/Injective_function" ). At best, they are describing some more general phenomenon which might correspond to holography in those cases where the mapping is invertible.
2) The holographic principle relates a quantum theory in the bulk space to another quantum theory on the boundary of that space. That is, in holography as conventionally conceived, you will have quantum uncertainty on both sides of the relationship. The only difference is that in the boundary theory, the quantum uncertainty is defined on top of a fixed space, but the bulk theory contains quantum gravity, so the metric and topology fluctuate as well. It's this extension of quantum uncertainty to space and time themselves which Craig Hogan hopes to detect, as "holographic noise".
So be aware that trying to derive quantum mechanics itself from the holographic relationship is a highly unusual idea, and possibly a wrong idea. Just to say it again: in holographic dualities as they are actually studied, there is already quantum randomness on the boundary, which extends to include space-time itself in the bulk theory on the other side of the equivalence. The innovative concept under discussion in this thread, as I understand it, is that we could start without quantum randomness on the boundary, and still end up with the appearance of quantum randomness in the bulk, because of the "local-to-nonlocal" aspect of the holographic mapping.
3) The origins of the holographic principle lie in the study of black holes. Without gravity, the number of possible states in a field theory will increase with energy as a function of spatial volume. But if one of your fields is gravity, then black holes will form at high densities, and the entropy (and therefore the number of possible states) of a black hole is a function of area (the area of the event horizon), not of volume. So a field theory containing gravity has to behave like an ordinary field theory in a space of one less dimension. That is the qualitative statement of the holographic principle, as proposed by http://arxiv.org/abs/gr-qc/9310026" .
It is a very interesting fact that 't Hooft is trying to explain quantum mechanics itself, and not just quantum gravity, using cellular automaton models in one less dimension. So I was wrong to say that the idea of a holographic explanation of quantum mechanics is entirely new; Gerard 't Hooft, a Nobel Prize winner and one of the many parents of the standard model of particle physics, is an exponent of this idea! But it should be understood that this is 't Hooft in the "later Einstein" phase of his career. Einstein spent the last decades of his life working on unified field theories and away from the mainstream of theoretical and experimental physics. With respect to the holographic principle, the 1997 discovery of AdS/CFT by http://arxiv.org/abs/hep-th/9711200" was a new stage in the development of the idea, because for the first time there was a quantitative example. Maldacena wasn't just proposing that a quantum gravity theory is equivalent to some unknown field theory; he was saying, string theory on a particular space is equivalent to a particular, already known field theory.
The years since then have involved the intensive study of these two theories, and the identification of many other dual pairs. But 't Hooft's recent work does not involve any of this. He is proceeding alone in a different direction.
So what about the people who are working on the concrete examples of holographic duality unearthed by Maldacena and others? They aren't trying to explain quantum mechanics. They take it as a given, and instead they use the duality between two quantum theories to learn about both. However, in some of the early papers by Arkani-Hamed et al (who I mentioned earlier in the thread), you will occasionally see the idea that maybe their new framework will even explain quantum mechanics. The usual headline for their approach is that they have abandoned manifest locality, and so perhaps they have found a level of description beyond space-time. But another feature of their Grassmannian formalism is that unitarity is not an input either. Unitarity is the feature which, in quantum mechanics, ensures that the probabilities add to one. So to have discovered a formalism in which unitarity doesn't have to be introduced may mean they have found something more fundamental than quantum mechanics. (Let me mention that their formalism involves twistors, and it was precisely Penrose's ambition to explain quantum mechanics as well as to go beyond space-time.)
In our discussion here we're saying, what if quantum mechanics only applies in the bulk, but the boundary is classical? However, in Arkani-Hamed's recent talks, he interprets their work as the discovery of a third framework, neither string theory (bulk) nor field theory (boundary), but something else outside space-time entirely (twistor space - perhaps it is as simple as that - twistors are the answer). And this is the framework where neither space-time locality nor quantum unitarity is "manifest", i.e. visible - you have to switch to the other perspectives to see them.
So if we take a hint from the stories of Einstein, 't Hooft, and Arkani-Hamed, and say that the best guide to the truth is to focus on the concrete quantitative example of holography which we are lucky enough to have (AdS/CFT), rather than just guessing - then that would imply that the genesis of quantum mechanics is to be found, not in the boundary-to-bulk transformation, but in the transformation from the "third theory" into either of the space-time descriptions, boundary or bulk.