Don't really care about the scheme or the statistics. People will talk a lot about these things, but the idea behind math and "theorems" (and, ironically, syntax) is to get around reasoning at a low level that the mind is poor at tracking. This means that "thought experiments" which resort to details in order to challenge an hypothesis are prone to be sort of like magic tricks: they seem to survive only as long as understanding is lacking.
For example, there once was a time when the smartest people on the planet were doing thought experiments about algebra, the properties of polygons, and transmuting lead into gold. They were typically either proven wrong or trivialized eventually, and the thought experiments vanished. So the mere existence of thought experiments--or even the drive to come up with them--is usually a discrete, infallible sign that the "theory" doesn't hang together, or is clouded with noise that makes it needlessly complex (Quantum Computing is likely the latter--and that is what we are talking about: quantum signal processing).
So I'm not addressing the scheme, but I'd like to highlight a few things in terms that are a bit more relevant than a physical science "theorem" in an unresolved domain: unclassified quantum computing/photonics.
A) Quantum superposition $=$ Quantum entanglement $=$ Quantum Coherence
B) It has recently been acknowledged that Quantum Coherence $=$ Optical Coherence (i.e., photon coherence is more or less the same thing as quantum coherence)
And, with holography and holographic techniques being regularly used and vanishing from scientific discourse under the auspices of national security for the last 60 years, it is perhaps safe to say that Photon Coherence is recorded and replayed all the time, and coherent (entangled) elections to boot! (every time a technique relying on electron holography is used, in fact)
So I don't know about this "no-cloning theorem." It sounds kind of like "no-fish on Fridays": one of those things people just say and do, but which no one can really find any justification for. Any how, I am sure there are many papers out there. But I am not sure why holography works, if coherence cannot be cloned. The universe--and anything that relies on a beam splitter--simply does not make sense otherwise.
And I am sure that our only source for the no cloning theorem are texts and symbols that only the most entrenched can decipher...that and inconclusive experiments with newly invented measurement techniques.
Holography, however, has been around since 1941, and is something you can do in your backyard as long as you spend a few bucks.
And I'll leave it with this: the arguments I have heard about the no cloning theorem (other than symbolic gibberish that purports to overcome issues in experimental error) relate to causality. And, where they relate to causality, they fall back on the old philosophical trope: how can a tree fall in the woods without someone there to observe it without violating causality?
And all of superposition, communication, light limited communication etc. follows from this philosophical kernel that, I think we can acknowledge, is meaningless when viewed under the light of a normal math proof.
Any iff mathematical concept must be proven in both directions: if you take schrodinger's cat and examine the superposition of the rest of the world relative to the cat when the cat's master decides to open the chest and take the cat out based on the decay rate of another isotope outside the chest, then infinite cats live and die, infinite scientists open the chest, and the universe explodes.
It is, however, possible for there to be only one universe if some aspect of the cat, the scientist, the isotope in the chest, and the isotope next to the scientist are zero distance from each-other, and in constant communication through some global information singularity. But that would introduce something else entirely. Which is the realm of sci-fi, and of course, infinite cats, scientists, Amys and Bobs living, dying and randomly sending FTL versions of Shakespeare with infinite quantum monkeys are much more reasonable.