Distinguish between measuring devices and 'sources of unitary evolution'? In a quantum optics lab, imagine that we are given with a collection of experimental tools to set-up an experiment on an optical table. This collection could consist of devices like photon detectors, phase shifters, beam splitters etc. In this collection, how can we distinguish between measuring devices and 'sources of unitary evolution'?  Can quantum theory tell which devices in our collection are devices capable of producing state reduction(measurement) from devices that merely produce some unitary transformation on the input state?
For instance how do we know that a transparent glass plate on the path of a laser beam can just produce some phase shift, whereas an opaque glass plate with a coating capable of fluorescence results in a measurement(where we have a state reduction)? Can we describe this differing capability of a transparent glass plate vs an opaque glass plate from quantum theory? Note that I am not asking for an explanation for the fact that an opaque glass plate absorbs most of the incident light in contrast to a transparent glass plate. That's well known. Rather, I want to know what's the distinction(if any) between a glass plate coated with a fluorescence material and a transparent glass plate, that makes the former device capable of producing state reduction?
 A:  Which devices produce measurements? 
An observable is measured if it produces a cascade of practically irreversible influences on the device and on the rest of the system. That's the definition of measurement.$^{[1]}$ Any device that allows an observable to produce such an influence is capable of measuring that observable.
Measurement is a physical process. In quantum theory, all physical processes are given by unitary time-evolution. Given a model (a set of observables and a Hamiltonian) and an initial state, quantum theory can tell us which physical processes occur, so it can tell us what measurements occur.$^{[2]}$
Of course, if we want quantum theory to tell us which devices are capable of producing measurement, then we need to include those devices (and maybe their surroundings, too) as part of the quantum system. That makes the math prohibitively difficult, but in practice, we don't need to do the math. Some basic intuition is sufficient.
Here's an example. When a photon passes through a transparant glass plate, the plate typically influences the photon (say, by producting a phase shift or refraction or reflection or whatever), but that's not a measurement of any property of the photon. To determine whether or not the photon is being measured, we need to think about what the photon does to the glass plate (or to the surroundings). If a given observable of the photon doesn't have any practically irreversible effect on the glass plate (or the surroundings), then that observable is not measured.
Here's another example: When a photon encounters something that can be used as a location-measuring device (aka detector), the photon initiates a practically irreversible cascade of influences that depends on the photon's location (for example). The practically irreversible cascade of influences is the reason we call it a detector. I'm being vague here because I don't know enough about optics equipment to be more specific, but the idea is always the same: to qualify as a measuring device, it must allow the photon to exert some type of practically irreversible influence on the rest of the system.
These examples describe physical processes, which quantum theory describes by unitary time-evolution. To diagnose the occurrence (or potential occurrence) of a measurement, we don't need state reduction. We just need the definition of measurement that was given above, combined with unitary time-evolution in a sufficiently comprehensive model.
 An ambiguity, and why it doesn't matter 
The definition of measurement given above is ambiguous. What exactly does "practically irreversible" mean? Exactly how bad must a measurement's fidelity be for us to stop calling it a measurement? It's ambiguous, and that's okay. The ambiguity didn't stop us from doing physics before quantum theory was developed, and it isn't stopping us now.
But if the definition of measurement is ambiguous, then how do we know exactly when we should apply the state replacment rule? We don't know exactly, and that's okay. Fortunately for quantum theory, a high-fidelity measurement is like popping a balloon: when a it occurs, it occurs so quickly and so irreversibly that it is practically unambiguous.$^{[3]}$ After such a high-fidelity measurement, we can safely apply Born's rule and the state replacement rule.
How soon after? It doesn't matter.$^{[4]}$ Whether we do it two seconds after, or two days after, or two years after, we'll get the same answer. This works because the physical process of measurement is practically irreversible, by definition. It's a unitary process, so it's reversible in principle, but it's practically irreversible, just like popping a balloon is practically irreversible. Once it happens, quantum theory never forgets that it happened, so we can apply the state-replacement rule at any time after the measurement event.

Footnotes
 $[1]$ The motive for this definition should be clear: we can't gain information about an observable that doesn't influence our measuring devices, and if the influence weren't practically irreversible, then our recording devices couldn't keep a reliable record of the results. This definition of measurement is appropriate in any theory. In quantum theory, it's also called   decoherence because of what it implies about the entanglement between the thing being measured and the rest of the world. 
 $[2]$ In contrast, quantum theory does not tell us when state reduction occurs. It's the other way around: we tell quantum theory when state reduction occurs. The connection between measurement and state reduction is this: when quantum theory tells us that a sufficiently high-fidelity measurement has occurred, then we can apply the state reduction rule with respect to whatever observable quantum theory says was measured. 
 $[3]$ A high-fidelity measurement occurs much more quickly than any balloon-pop. Anecdotally, a high-fidelity measurement is among the fastest process in nature. This is a prediction based on unitary time-evolution in models that include the microscopic dynamics of macroscopic measuring devices, and this prediction is consistent with real-world experience. 
 $[4]$ It doesn't matter as long as we remember to evolve the projection operator forward in time, using the same unitary time-evolution operators that we use to evolve any observable forward in time, and as long as we apply the projection operators in the correct chronological order (if we're dealing with multiple measurements), because they typically don't commute with each other. 
