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  Measurement of a System by Multiple Quantum Probes

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Assume that variable A, of quantum probe 1, interacts and entangles with variable B, of system S, to be measured. After the interaction, the probe travels to a detector. This detector can measure A, to arbitrary accuracy and, knowing A, we can determine the (reduced) range of possible B values. The momentum of the probe, in the direction of the detector, is not affected by the entanglement. Let's also assume that this is a QND measurement, so after the measurement is completed, for all intents and purposes, B does not change as a result of any back action.

After the above interaction/entanglement is completed, but before probe 1 arrives at the detector, quantum probe 2's variable A entangles with S's variable B. Further, assume that the distance from the system to the detector, along with the momentum expectation values and uncertainties of each probe, is such that either probe could arrive at the detector first. 

If probe 2 is measured at the detector first, then when probe 1 is subsequently measured, will it refine the measurement of B that was made by probe 2, even though probe 1 interacted with S before probe 2 did? I think the answer is yes, after modeling the whole scenario with Schrodinger's equation, but just want to make sure. 


asked Mar 3, 2016 in Theoretical Physics by daveinri (0 points) [ revision history ]

Weird things may happen, particularly if $B_{System}$ is unchanged after the QND measurement. Is it not merely a classical context with 2 not perturbative measures ?

@IgaeI  Thank you for your response! I think this is different than perturbation theory, which I understand is for problems that are hard to solve in a straight forward way. The specific cases I looked at, with their interaction Hamiltonians, were pretty easy to solve, as far as I could tell, and my solution was that the probes did not have to be measured in the order in which they interacted with the system in order for the second probe measured to refine the results of the first probe measured. 

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