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Physics
Quantum Physics
Quantum Interpretations and Foundations
What does delayed choice entanglement swapping require?
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[QUOTE="vanhees71, post: 6828748, member: 260864"] Indeed, the entanglement swapping only works if you have an entanglement between 1&2 (Alice) and 3&4 (Bob). You can think of realized these as two entangled photon pairs (all together a four-photon state). As an example take the state $$|\Psi \rangle = \frac{1}{2} [\hat{a}^{\dagger}(\vec{p}_1,+1) \hat{a}^{\dagger}(\vec{p}_2,-1)-\hat{a}^{\dagger}(\vec{p}_1,-1) \hat{a}^{\dagger}(\vec{p}_2,+1)][\hat{a}^{\dagger}(\vec{p}_3,+1) \hat{a}^{\dagger}(\vec{p}_4,-1)-\hat{a}^{\dagger}(\vec{p}_3,-1) \hat{a}^{\dagger}(\vec{p}_4,+1)]|\Omega \rangle.$$ If you then use the photons with momenta ##\vec{p}_2## and ##\vec{p}_3## (at V's place) to make a Bell measurement and measure only photons with momenta ##\vec{p}_1## and ##\vec{p}_4## where V got one out of four possible Bells states, you'll see that this subensemble is described by a Bell state for photone ##\vec{p}_1## and ##\vec{p}_4##. It doesn't matter when you do this choice. You can use a measurement protocol for all 4 photons and post-select each of the four possible projections to Bell states of V's photons. I think the only consistent interpretation, given the microcausality property of QED and the success in using QED to predict the outcome of this experiment, is that indeed the cause of the correlation between photon 1 and 4 in each of the sub-ensemble is due to the preparation of the four-photon state in the state ##|\Psi \rangle## given above. A real experiment of this kind is given here: [URL]https://arxiv.org/abs/0809.3991[/URL] [URL]https://doi.org/10.1103/PhysRevA.79.040302[/URL] [/QUOTE]
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Quantum Interpretations and Foundations
What does delayed choice entanglement swapping require?
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