Are photon probability amplitudes entangled in a two-filter setup?

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Discussion Overview

The discussion revolves around the concept of photon probability amplitudes in a two-filter setup, specifically whether the filters (acting as sources) are entangled or if the photons themselves are entangled. The context includes theoretical considerations related to quantum electrodynamics and the treatment of photon states.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant proposes treating the photon source as time evolving rather than as a static photon state, referencing Feynman's work in QED.
  • The same participant suggests that after passing through a narrow bandwidth filter, the photon probability amplitude undergoes coherent evolution, leading to the question of whether the second filter is entangled with the first.
  • Another participant seeks clarification on whether the inquiry pertains to the entanglement of the sources (filters) or the photons themselves.
  • The initial poster clarifies that they are specifically asking about the entanglement of the sources (filters) rather than the photons.
  • A later reply indicates that the entanglement consideration applies once the light has arrived at the second filter.

Areas of Agreement / Disagreement

Participants are discussing the nature of entanglement in the context of the filters and photons, but there is no consensus on the specifics of the entanglement or the implications of the setup.

Contextual Notes

The discussion involves assumptions about the coherent evolution of photon probability amplitudes and the definitions of entanglement in relation to sources and photons, which remain unresolved.

zonde
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I have thought for some time that it is physically correct to treat photon source as time evolving rather than photon state (i.e. using Heisenberg picture rather than Schrödinger picture) so I was glad to find this picture in Feynman's book (QED: The Strange Theory of Light and Matter):
Nm18NbB.png

In this picture (b) there is space time diagram that shows time evolution of photon's probability amplitude at source. So I confirmed for myself that the idea is fine.

But I want to go a bit further based on this diagram. Say we have light source with broad spectrum.
After light source we place narrow bandwidth filter. So we can view this filter as monochromatic light source where photon probability amplitude undergoes coherent evolution.
But after this filter we place another identical filter that becomes new monochromatic light source. It has to undergo time evolution coherently with the first filter, right? Or in other words are they entangled?
This is the question I wanted to ask.
 
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Are you asking if the sources are entangled or the photons are entangled?
 
Jilang said:
Are you asking if the sources are entangled or the photons are entangled?
I am asking about sources (filters). We could talk about single photon in this example so there is no point talking about photon entanglement.
 
I should say so then, at least once the light had arrived at the second filter.
 

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