How to Shut Up and Calculate a Delayed Choice Outcome

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SUMMARY

The discussion focuses on the application of evolving Hilbert space formalism in calculating outcomes of delayed choice experiments in quantum mechanics. The user seeks a simplified method to apply these principles to toy problems involving two-photon sources and optical elements like U1A, U2A, and U1B. The goal is to calculate expected statistics, such as coincidence counts, influenced by the configurations of these optical elements. The conversation emphasizes the need for a practical approach to understanding complex quantum phenomena without mastering the entire formalism.

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  • Understanding of Quantum Mechanics principles
  • Familiarity with Hilbert Space formalism
  • Basic knowledge of Feynman path integrals
  • Experience with optical elements in quantum experiments
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  • Research simplified models of delayed choice experiments
  • Learn about two-photon interference and coincidence counting
  • Explore the mathematical framework of evolving Hilbert spaces
  • Study the impact of optical transforms on quantum states
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Quantum physicists, students of quantum mechanics, and researchers interested in the practical applications of quantum theories in experimental setups.

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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?
 
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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?

delayed.png


P.S. I think I know how to shut up, but I really don't know how to calculate.
 
Or, simpler and better, assuming electrically (classically) modulated U1A and U2A devices:

delayed2.png
 

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