How to Shut Up and Calculate a Delayed Choice Outcome

[Swamp Thing]

Googling for some unrelated topic, I stumbled upon Quantum Mechanics in an Evolving Hilbert Space.

A lot of the math in this paper is beyond my present level, but some of the more descriptive passages made intuitive sense to me.

Based on this, my question is, is the formalism of an evolving Hilbert space a useful tool to describe (and calculate!) delayed choice experiments?

And if so, is there a simplified way to apply the basic principle to toy problems with one or two particles, without necessarily mastering the formalism in its entire awful majesty?

 

[Swamp Thing]

For example, say we have a two-photon source as shown below. U1A, U2A and U1B are optical elements (transforms) that could modify the prepared state in some way -- they would control the phases of various Feynman paths and thus control various interference effects.

But the world lines of U1A and U2A are such that we have effectively a delayed substitution of one for the other. If all the world lines are defined, how do we calculate the expected statistics such as coincidence counts etc which we know to be functions of U1A, U2A and U1B?

P.S. I think I know how to shut up, but I really don't know how to calculate.

 

[Swamp Thing]

Or, simpler and better, assuming electrically (classically) modulated U1A and U2A devices: