wolfgang proposed a similar example on Scott's blog:

I wonder if we can turn this into a real physics problem:

1) Assume a large-scale quantum computer is possible (thinking deep thoughts, but not really self-conscious as long as its evolution is fully unitary).

2) Assume there is a channel which allows enough photons to escape in such a way to enable consciousness.

3) However, at the end of this channel we place a mirror – if it is in the consciousness-OFF position the photons are reflected back into the machine and unitarity is restored, but in the consciousness-ON position the photons escape into the deSitter universe.

4) As you can guess we use a radioactive device to set the mirror into c-ON or c-OFF position with 50% probability.

Will the quantum computer now experience i) a superposition of consciousness and unconsciousness or ii) will it always have a “normal” conscious experience or iii) will it have a conscious experience in 50% of the cases ?

Scott responded that

I tend to gravitate toward an option that’s not any of the three you listed. Namely: the fact that the system is set up in such a way that we could have restored unitarity, seems like a clue that there’s no consciousness there at all—even if, as it turns out, we don’t restore unitarity.

This answer is consistent with my treatment of other, simpler cases. For example, the view I’m exploring doesn’t assert that, if you make a perfect copy of an AI bot, then your act of copying causes the original to be unconscious. Rather, it says that the fact that you could (consistent with the laws of physics) perfectly copy the bot’s state and thereafter predict all its behavior, is an empirical clue that the bot isn’t conscious—even before you make a copy, and even if you never make a copy.

Was Alice conscious in case 1? In case 2? Since the sequence of events in both cases were in fact the same exact sequence of events - not merely identical, but referring to the exact same physically realized sequence of events - up to our quantum coinflip, it's nonsense to say that one was conscious and the other was not.

Well, Scott :

that you and I are conscious seems like a pretty clear paradigm-case. On the other hand, that you and I would still be conscious even if there were aliens who could perfectly copy, predict, reverse, and cohere us (very likely by first uploading us into a digital substrate), seems far from a paradigm-case. If anything, it seems to me like a paradigmatic non-paradigm-case.

I disagree with his caveat for consciousness, since I would like to think of myself as conscious even if I am a simulation someone can run backwards, but I am not 100% sure, because reversibility changes the game considerably. Scott alludes to it in the Schrodinger's cat experiment, by noting that death becomes reversible (in the QM-sense, not the cryonic sense), and thus largely loses its meaning:

I claim that there’s no animal cruelty at all in the Schrödinger’s cat experiment. And here’s why: in order to prove that the cat was ever in a coherent superposition of |Alive〉 and |Dead〉, you need to be able to measure it in a basis like {|Alive〉+|Dead〉,|Alive〉-|Dead〉}. But if you can do that, you must have such precise control over all the cat’s degrees of freedom that you can also rotate unitarily between the |Alive〉 and |Dead〉 states. (To see this, let U be the unitary that you applied to the |Alive〉 branch, and V the unitary that you applied to the |Dead〉 branch, to bring them into coherence with each other; then consider applying U-1V.) But if you can do that, then in what sense should we say that the cat in the |Dead〉 state was ever “dead” at all? Normally, when we speak of “killing,” we mean doing something irreversible—not rotating to some point in a Hilbert space that we could just as easily rotate away from.

Since this changes at least one fundamental concept, I am reluctant to state that it cannot apply to another.