Is a communications channel based on quantum mechanics as effective as one based on any other physics? What I mean by effective in the question refers to the time and space requirements for sending information over a quantum communications channel. Having read "Mike and Ike" but doing no independent research on the question, my initial impression is that a channel using an effect from quantum field theory e.g. quantum electrodynamics would be more powerful over a narrower range of algorithms than an "ordinary" or "vanilla" quantum computer i.e. one that derived information from its steady-state behavior e.g. quantum electrostatics.  
Are there any quantum information theorists working on proving whether this is true or false? 
EDIT:
Allow me to quote from the portion of the book the provoked the question (p.6):

At the time of writing it is not clear whether Deutsch’s notion of a Universal Quantum
  Computer is sufficient to efficiently simulate an arbitrary physical system. Proving
  or refuting this conjecture is one of the great open problems of the field of quantum
  computation and quantum information. It is possible, for example, that some effect of
  quantum field theory or an even more esoteric effect based in string theory, quantum
  gravity or some other physical theory may take us beyond Deutsch’s Universal Quantum
  Computer, giving us a still more powerful model for computation. At this stage, we
  simply don’t know.

I simply assume that a more powerful model of computation would give rise to a more efficient communications channel. Unless there has been a proof of the universality of a Universal Quantum Computer it seems that whoever said 'quantum is quantum' is very much getting ahead of themselves. 
Now, with all that being said, I reiterate my previous question: are there any quantum information theorists working on proving whether this is true or false? 
 A: Every single fiber optics cable in the world is a quantum channel. So a large percentage of information is currently being transmitted over quantum channels.
To explain further, the equations describing how the light propagates down the fiber optic cable are quantum.  Theoretically, quantum information can be transmitted over fiber optic channels. Quantum cryptography can be used to distribute secret keys across a fiber optic cable, something which cannot be done with classical channels.
We currently treat fiber optic cables as classical devices for the purposes of communication. One can ask how much using the quantum effects would raise the amount of information that we could send using a given energy, and in the range of parameters which they are currently being used, the answer is "not much". And experimentally, we don't have anywhere close to the input devices and output devices that we would need to send real quantum information over fiber optical cables. If we could, we might be able to use this to build better telescopes. 
A: Would Quantum Field Theory allow more powerful computation than the standard quantum computing model ?
The question above is how I understood your question after your edit. It is the question I try to answer below. 
As far as I know, the question is still formally open since it was asked in Nielsen and Chuang's book. However, in the 13 years (2000-2013) since the publication of this books, progress have been made. This 2000 paper deal with the simulation of topological field theories and this one from 2011 deals with scalar field theories. Both paper provide efficient simulation algorithm (to run on a quantum computer) of some quantum field theories, thereby showing that these theories do not allow to create a computer more powerful than the standard quantum computer.
If you want an accessible account on this question, you can read this answer by @Scott Aaronson, on cstheory.sx and this post on his blog.
A: I'm not sure what is meant by 'quantum electrostatics' or what a 'vanilla' quantum computer is.  Cutting edge quantum computers are not very capable or efficient today compared to classical (semiconductor) computers.
That said, quantum computing does offer communications and encryption (as well as computation and cryptography) mechanisms that can not be replicated using just classical channels, at least in theory.  In practice, thus far, quantum computers are not a practical choice.
