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In the "classical" imaginary Schrodinger's cat experiment, which seems to be no longer serious, or at least irrelevant, by many (some?) people, everything is explained away by decoherence.

Now, let us change the experiments and replace the classical decaying radioactive element by some variation that is isolated from the environment and thus its decoherence time is as large as we want. Same with the cat, let us replace it by a quantum computer that is computing but will be break and stop computing after the decay.

Now, everything inside the box is isolated from decoherence.

Question: Assume the box is closed. Can we still say that the quantum computer is in a pure state, in which both computing and broken are superimposed at the same time? (will a simulated cat be dead and alive at the same time?)

PD: I think what actually happens should be important, because as computer power grows, we will be able to simulate virtual beings in their environments, and unless you believe that only computers made of "meat" can have subjective experiences, the revamped cat gedanken might become relevant again

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  • $\begingroup$ Saying that "there is no decoherence" is clearly absolutely equivalent to the statement "one has to use a pure state and remember all the superpositions and relative phases". On the other hand, I also feel that you underestimate how impossible is to remove the decoherence from the whole system. Quantum computers don't remove decoherence from "everything"- just the decoherence of the degrees of freedom they are using to calculate. Realistically, any macroscopic piece of material at a temperature visibly different from absolute zero'll have some degrees of freedom that decohere almost instantly $\endgroup$ – Luboš Motl May 20 '16 at 17:43
  • $\begingroup$ @LubošMotl isn't the decoherence of non-calculating degrees of freedom irrelevant? you can change the question to keep those, which are the ones who decide if the computer stops calculating. Or am I wrong? $\endgroup$ – user83548 May 20 '16 at 17:50
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    $\begingroup$ I think that you implicitly make a mistake by assuming that once the computer-cat is "broken", it ceases to obey the laws of QM. But by the assumption of no decoherence, it never does. $\endgroup$ – Luboš Motl May 20 '16 at 18:00
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    $\begingroup$ Note that David Deutsch had already considered a similar thought experiment. This involves simulating a virtual observer measuring the z component of a virtual spin polarized in the x-direction. It is then easy to demonstrate that you can erase the results of the measurement but with a record kept about the fact that a measurement was actually carried out, the transform is unitary therefore it can be implemented inside the quantum computer. However, both branches where the observer found spin up and spin down contribute to the final state where the original spin state is restored. $\endgroup$ – Count Iblis May 20 '16 at 19:08
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    $\begingroup$ Since the observer can verify that the spin has been restored in the original state (e.g. by repeatedly doing the experiment and making measurements on the final state), this verifies that both branches exist and that the observer did find spin up and spin down after which his memory was partially wiped out by the unitary transform. $\endgroup$ – Count Iblis May 20 '16 at 19:10
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Following Lubos' comments, it is clear that your problem is equivalent to two quantum computers exchanging signals (or equivalently, a single one with a halting state).

If your question is: Will the simulated cat be "alive" (that is, enjoying his simulated life), or "dead" (that is, the computer has halted and the cat no longer experiencing a simulation) simultaneously, then the answer is yes.

Decoherence has not solved the measurement problem yet, it only tells you that once you (or the environment) interact with the computer, it will quickly decohere into a specific state (that is, the computer either calculating or not calculating).

As to what the cat experiences: who knows?

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I think Schrodinger's cat experiment is a word conundrum rather than reality. For example, it took 1000 years for philosophy to prove that a man could run faster than a tortoise. I.E., Achilles and the tortoise: In a race, the quickest runner can never overtake the slowest [if had a head start], since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. – as recounted by Aristotle. The only difference here is we KNEW the man could overtake the tortoise in reality, so could see the absurdity, even though at the time, it could not be proved wrong. But in the Schrodinger example we don't know and can't see the possible absurdity of the question.

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