What Happens to Entangled Photons at a Beam Splitter?

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SUMMARY

The discussion centers on the behavior of entangled photons at a beam splitter, specifically when photons are converted to the 45/135 basis using a wave plate. The participants analyze the combination of basis states from two pairs of entangled photons as they interact at the beam splitter. The key challenge identified is determining the overall state after the beam splitter while maintaining the entanglement with their original partners. The proposed state after the beam splitter is expressed as -|45>i|45>(b) + -i|45>|45>(c).

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  • Understanding of quantum entanglement and photon states
  • Familiarity with beam splitter operations in quantum optics
  • Knowledge of wave plate functions and basis transformations
  • Proficiency in quantum state notation and manipulation
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Quantum physicists, optical engineers, and students studying quantum mechanics who are interested in the behavior of entangled photons and their interactions at beam splitters.

StevieTNZ
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Okay, I have the following scenerio (attached picture).

The inputs for path b and c are two photons. both photons aren't entangled with each other - they're entangled to other photons. Before the beam splitter there is a wave plate that converts the photon into the 45/135 basis.

So what we end up with is taking each basis state and add it to each of the other basis states of the other pair of entangled photon when figuring out what happens at the beam splitter.

I'm a bit confused on how to work it out. Because the photons remain entangled with their original partners, how do we write the overall state after the BS?

Take |H>|45> for path b and combine it with -|V>|45> on path c. Combine only the |45>'s at the beam splitter. So we end up with -|45>i|45>(b) + -i|45>|45>(c)?
 

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