I have some practical difficulties with projective measurements, so I'd welcome inspiration from others. This is beyond the question "Are true Projective Measurements possible experimentally?" in that I'm not aiming for perfection but for something practical. In particular, I care about the case where we want to keep computing after a measurement.

Let us say we try to effect an upwards transition between two energy levels, by illuminating the sample with the appropriate wavelength. The transition is only possible if the initial state is occupied, since the final state is outside of out computational basis. For this to be a projective measurement rather than an unitary operation in a larger basis, we need to irreversibly detect this, say by a radiative spontaneous relaxation of this "final" state of the transition to a third energy level. If we were subsequently able to go back to the original level (coherently and rapidly), then I assume we'd have a messy work-around for an ideal projective measurement.

The question is: can this be done, or is this scheme fundamentally flawed? If it can be done, please illustrate with examples where this works.


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