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How do two light beams, one squeezed in phase and the other in amplitude, superposed on a beamsplitter, result in an EPR entangled state?

Physics Asked by Quantum Journalist on December 25, 2020

I have found this information in Section 4 of this paper: https://www.degruyter.com/view/journals/nanoph/5/3/article-p469.xml?language=en

Also on Wikipedia https://en.wikipedia.org/wiki/Squeezed_states_of_light#Entanglement-based_quantum_key_distribution

And here in Figure 1 https://arxiv.org/pdf/1508.06462.pdf

That combining two squeezed light beams with a phase difference of 90 degrees (pi/2 radians) on a beamsplitter and will generate two entangled beams at the output that can be measured with homodyne detection, their quantum uncertainties in phase and amplitude will be correlated.

Here is a more general description of states entangled in phase and amplitude called continuous variable entanglement http://gdriqfa.unice.fr/IMG/pdf/Laurat_ENT_invited-talk_GDR-IQFA_Nice_March2011.pdf.

And I do not understand the logic behind it. Bell state measurement is supposed to be probabilistic, for example when swapping entanglement between two photon pairs entangled in polarization emitted by a nonlinear crystal.

Here it says continuous variable entanglement is deterministic, as opposite to probabilistic. How is it possible?

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