I What is CV Bell State Measurement and How Does Entanglement Swapping Work?

[James2018]

TL;DR Summary

Continuous variable Bell state measurement

There is something I don't understand called CV Bell state measurement.

In these two experiments they get two entangled beams

"by overlapping phase-squeezed light with amplitude squeezed light with a phase difference of pi/2 at a 50-50 beamsplitter"
See Figure 11
https://www.researchgate.net/publication/303852805_On-chip_continuous-variable_quantum_entanglement

and
"We generate a pair of entangled beams from the interference of two amplitude squeezed beams."
https://arxiv.org/pdf/quant-ph/0209001.pdf

Of course, the reason they use non-linear crystals is because this is the way to generate amplitude-squeezed light and phase-squeezed light, which have less amplitude noise or phase noise than a coherent light state.

Also, they swap entanglement between laser light and a mirror generated by radiation pressure to the entanglement between the two mirrors by detecting the interference results after a beamsplitter. If you look at Figure 1, it compares this experiment to the above two.
https://arxiv.org/abs/1508.06462

I do not understand how entanglement can be swapped simply by interference of two light beams that are entangled to something else. Also, I don't see any post-selection being mentioned like I see in polarization entanglement swapping.

 

[James2018]

There may be some equations on page 12 and 13 here https://arxiv.org/pdf/quant-ph/0410100.pdf
where it says " The two-mode squeezed vacuum state, as produced by the unitary two-mode squeeze operator in Eq. (71) corresponding to the NOPA interaction Hamiltonian in Eq. (70), is equivalent to the two-mode state emerging from a 50:50 beam splitter with two single-mode squeezed vacuum states at the input "

And some sumary of the mirror experiment here https://physicsworld.com/a/plan-for-supersized-entanglement-is-unveiled-by-physicist/
" This entanglement is then “swapped” to become an entanglement between the two mirrors. This is done by measuring the interference of the two light beams as they exit the interferometer. Crucially, this measurement provides information about the nature of the entanglement but does not destroy it because the measurement does not provide any information about an individual mirror. "

 

[James2018]

Oh and I forgot to mention that
" Outputs are entangled EPR1 and EPR2 beams when the incident squeezed light beams SL1 and SL2 are combined with relative phase ϕ of 90°. Outputs are two independent squeezed light SL1 ′ and SL2 ′ when the squeezed light beams SL1 and SL2 are combined with ϕ of 0°. "

Which is more confusing to me as why.