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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 ...

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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) ...

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Decoherence of a single wave function to a new state, for two particles after scattering, let us say, does not mean that the two outgoing particles are no longer described quantum mechanically. They will have new functions arising from the solution of the equations for new boundary conditions. So 1) is correct. It is when one describes quantum ...

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Decoherence solves the pragmatical questions: You have a system, it interacts somehow a little bit with the environment, you cannot control and measure the environment, and you want to know when the interaction with the environment effectively destroys any interference effects. So, it describes how a pure state $\psi = \sum f_a \psi^a$ becomes something like ...

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Weak measurements don't let you learn about the system without disturbing it. They let you make tradeoffs, where you disturb/decohere/collapse less by revealing less, but you still have to pay for whatever the measurements do reveal. You can't combine many weak measurements into a "free" strong measurement. But say Alice weakly measures X, and learns ...

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It's a case of bad labeling: the $i$,$j$ labels in Fig.1 and Eqs.(4-5) have different meaning. In addition, subscript 1 was dropped on all $B$'s in Eq.(5). Other than that, it's straightforward algebra: Start by rewriting the final result of Fig.(1) in the familiar operator-product form, expand, and rearrange:  \overline{\left[ E \cos(B_1\tau) - i {\hat ...

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