So usually when you talk to physicists who accept the multi-world interpretation of quantum mechanics they claim that the measurement is reversible if you take into account the worlds we don't observe. Driven by this line of thought I think I can show if one alternates between measurements of $2$ different observables say $A$ and $B$ and do $2N$ (where $N$ is a large number) such measurements in time $T$. One is also allowed to assume the underlying dynamics, i.e. some Hamiltonian under which the system evolves. Then I claim it is impossible to reconstruct the original density matrix unless one knows when the measurements took place to an accuracy of $(\frac{T}{2N})^2$. Is there something like this in the literature?

  • $\begingroup$ I see none combine the multi-world interpretation with a rather real-life application before. To get the density matrix of a quantum state(which is observable) you do quantum state tomography to achieve so. $\endgroup$ Dec 18, 2020 at 6:36
  • $\begingroup$ Reason for downvote? $\endgroup$ Dec 18, 2020 at 15:52
  • $\begingroup$ Nope, that's not me. $\endgroup$ Dec 19, 2020 at 5:59
  • $\begingroup$ I don't see how this can work. I suppose you are talking about successive measurements, so you don't reset the state between the measurements. If this is the case, at the second measurement (say, measuring $B$ here) you are already not measuring the initial state $|\psi\rangle$ anymore, but rather the state on which it collapsed after measuring $A$. There is no more information about $|\psi\rangle$ to recover other than that obtained with the first measurement. $\endgroup$
    – glS
    Dec 19, 2020 at 19:33
  • $\begingroup$ @YitianWang You haven't read much of David Deutsch then. His work (including developing the quantum circuit model still used today) is almost entirely based on the application of MWI to real-life applications. $\endgroup$ Dec 20, 2020 at 3:20


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