It has implications for morality if the existing definitions of consciousness turn out incorrect or incomplete. It has implications for singularity technologies of mind uploading and cryonics revival if a theory of consciousness can be extended to predict end-of-identity. It's also simply interensting in its own sake.
We had a bad mix or two, of consciousness and QM in the past, already.
Some people demanded a conscious observer to collapse the wave function!
And some people talked about the "quantum nature of consciousness" quite a lot.
Both were quite unnecessary.
I am not saying, that it is therefore forbidden to think about the consciousness and QM at the same time, but that it should be done cautiously, very cautiously, to avoid old mistakes.
Max Tegmark publishes a preprint of a paper arguing from physical principles that consciousness is “what information processing feels like from the inside,” a position I've previously articulated on lesswrong. It's a very physics-rich paper, but here's the most accessable description I was able to find within it:
The whole paper is very rich, and worth a read.