Which implies an inverse mapping from ontologically definite states of consciousness, to a set of exact microphysical states, which are the physical states (or state, there might only be one) in which that particular state of consciousness is realized.

This would be pretty spooky to me if it was possible. My current expectations (call this B>Q>P) are:

|brainstates| > |qualiastates| > |phenomenonologystates|

If my expected ordering is right, then an inverse mapping from qualiastates to brain states should be impossible by the pigeonhole principle...

I think that there was a miscommunication here. To be strictly correct, Mitchell should have written "Which implies an inverse mapping from ontologically definite states of consciousness, to sets of exact microphysical states...". His additional text makes it clear that he's talking about a map f sending every qualia state q to a set f(q) of brain states, namely, the set of brain states b such that being in brain state b implies experiencing qualia state q. This is consistent with the ordering B>Q>P that you expect.