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This is a question about indirect quantum measurement, involving an observable of an object of interest and a probe that is used to measure that observable. In this experiment, an observable of the probe (for example the y component of probe's momentum) becomes entangled with the observable (for example charge) of the object of interest, at time t0. Between t0 and t1, the probe is in transit to the detector. At t1, the probe's momentum is measured, which results in a "state reduction" of the wave function, or density matrix, of the charge of the object of interest. By state reduction, I mean a reduction in size of the continuous range of charge states that have non-zero probabilities.

My question is: At t1, when the probe is measured, does the wave function, or density matrix, of the charge get "reduced" at that time? Or, at t1, when the probe is measured, does the wave function, or density matrix, of the charge get reduced retroactively back in time, at t0, when the entanglement occurred and the probe picked up the info it was carrying about the charge of the object of interest? (I imagine the former, but just checking).

In any case, maybe there have been some experiments to indicate when state reduction occurs for an indirect, probe-based, measurement. If not, I am curious about what you think that your favorite interpretation would say about, once the probe is measured, whether or not the state reduction of the observable of interest that the probe is entangled with takes place 1) retroactively, back in time, at the time of entanglement of the observable of interest with the probe 2) at the time of the measurement of the probe, or 3) at some other time.

Thanks,

Dave

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  • $\begingroup$ Since collapse is not a feature of all interpretations of quantum mechanics, you'll have to stipulate the interpretation you are considering for this to be answerable. $\endgroup$ – ACuriousMind Nov 17 '15 at 2:55
  • $\begingroup$ Please see rewording. I replaced "collapse" with "reduced", in order to avoid issues of quantum theory interpretation. All interpretations (Copenhagen, Multiverse, etc.) recognize "state reduction". $\endgroup$ – David Nov 17 '15 at 6:32
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    $\begingroup$ I don't understand what the reduced density matrix has to do with it - it just describes the state of a subsystem (i.e. what I see when I ignore all other parts of the system). $\endgroup$ – Martin Nov 17 '15 at 14:10
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The state is "measured" in the sense you are imagining - that is, it becomes definite - at whatever time it becomes possible in principle to infer its having a particular measurement outcome. In your case, if the probe provides unambiguous information about the measurement result, the time of measurement will be found to have been delta-t back in time. This is somewhat interpretation-dependent.

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  • $\begingroup$ AGML, thank you for your response! I guess it is hard to avoid interpretations, but if the state reduction of the object of interest occurs at the time of entanglement of the probe with the object of interest, rather than at the time of the measurement of the probe, then any interactions that occurred with the object of interest, between the time of entanglement with the probe and the time of measurement of the probe, must be "revised" after the probe is measured... That implication I find kind of confusing. $\endgroup$ – David Nov 17 '15 at 6:48
  • $\begingroup$ @David en.wikipedia.org/wiki/Delayed_choice_quantum_eraser $\endgroup$ – AGML Nov 17 '15 at 6:53
  • $\begingroup$ Thank you for the pointer. I will read carefully to see how closely it relates. In any case, it looks interesting. $\endgroup$ – David Nov 17 '15 at 7:09

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