Colin,
"Treating the quantum correlation as a problem in communications and signal processing is a novel approach..." all too true, unfortunately, even though Information Theory is now 70 years old. In My 2012 FQXi essay, I noted that "In one of the great scientific tragedies of the past century, "Modern Physics" was developed long before the development of Information Theory."
"it would have to approach perfection..." That is what error detection and correction coding is all about. Shannon proved (at least in the case of a multi-bit signal) that it should always be possible to create such a code, resulting in perfect detection, right up to the Shannon limit. The final generation of telephone modems (before they became obsolete) came pretty close.
"...making selections to eliminate higher harmonics, while leaving the lowest harmonic untouched..." In another context, this is exactly what raised-cosine filters and square-root-raised-cosine filters are all about: placing nulls at discrete points, to completely eliminate unwanted components, while completely preserving the desired fundamental, and without requiring an impossibly sharp filter cut-off.
"there must be some deep involvement in quantum phenomena which has been overlooked" Exactly. I believe the fact that Shannon's very definition of a "single bit of information" turns out to be the Heisenberg Uncertainty Principle, is that overlooked item: you cannot make multiple, independent measurements, on a single bit of information.
Another second thing that has been overlooked, is that:
The "squared" Fourier transforms at the heart of the mathematical description of every wave-function, are equivalent to the mathematical description of a histogram process, which is why the process yields probability estimates (the Born Rule) - regardless of the nature (particle or wave) of the entities being histogrammed. In other words, the math only describes the histogramming of observed events, not the nature of the entities causing the events, as has been assumed, in the standard interpretations of quantum theory. When you compute a Power Spectrum, you get the total energy accumulated in each "bin". And when the input arrives in discrete quanta, dividing the MEASURED energy in each bin, by the energy/quanta, enables one to INFER the number of received quanta in each bin. There is no INTERFERENCE pattern. Rather, there is an INFERENCE pattern. And if you compute the Power Spectrum of a double (or single, or triple...) slit's geometry, you get the famous INFERENCE pattern: independent of either quantum or classical physics. Particles/waves striking the slits merely act like radio-frequency carriers. All the information content within the INFERENCE pattern, is spatially modulated onto those carriers, by the slit geometry. In other words, the pattern is a property of the slits themselves, not the things passing through the slits.
A third and related overlooked item, is that QM only describes the statistics of DETECTED entities. It does not describe undetected entities at all. That is why it is unitary. Probabilities will always add to unity, when you only compare them to observed counts, that have been normalized via the number of DETECTED entities.
Rob McEachern