In fact, I'm working on a thesis project on Quantum Information and precisely on quantum error correcting codes. I just started not long ago my research on the subject, and specifically how one can go from a classical signal to a quantum signal to describe the algorithms of error correction codes in physical channels.
the following text may be of help to you, it contains a good mathematical analysis of quantum error correction codes in the relevant chapters. quantum computing: from linear algebra to physical realizations , authors: mikio nakahara and tetsuo ohmi, reference to original articles you can find in the book itself.
There is a lot of work going on here, it is a very active field of research. Also your question does not seem clear. Do you mean the uploading of classical information with a quantum oracle (alike Quantum RAM?)
As a first part of my work on the subject I make a comparison between the CECCs and the QECCs. After that I will adapt quantum error correction to specific channels in quantum systems. the subject has a good relationship with quantum information processing and quantum communication.
Hm, that might be a tricky comparison. In Quantum there is topological error correcting, but also a sort of 'colour' error correcting. And error corrections for specific bit flips. In that sense it is more elemental than classical error correction, which is basically utilizing compression and correction codes based upon mathematical formalisms. Such methods are not available for quantum as we cannot arbitrarily read qubits. But I'm interested if you do find some concrete parallels.
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