zonde said:
Wrong
If you measure photon 2 in 45 basis and 3 in 135 basis then photons 1 and 4 will have positive correlation for +45 and +135 measurement and negative correlation (minimal rate of four-fold coincidences) for +45 and +45 measurement.
So we have photons 1 and 2, and 3 and 4 entangled. We send 2 and 3 to beam splitter and we hope they get combined (I'm assuming the authors do this to create the four photon entanglement). Is this four-photon entanglement? From the title of the paper, I'm sure they're speaking of all four photons, 1,2,3,4 as entangled with each other. So if so, is the entangled state is the |GHZ> given? I fail to see photon 2 taking on 45 and 3 taking on 135 being possible if described by this state, when you 'sum over' (45+135)(45-135)(45-135)(45+135)+(45-135)(45+135)(45+135)(45-135).
But you can talk about projecting a certain bell-state onto the photons. I want to measure 2 in |45> and 3 in |135> without doing any projecting of bell states. Surely this is possible? I'm interested in what is possible if four photons are entangled, which I assume is described by |GHZ>.
Of course to ensure you have the |GHZ> state, you need to make sure you detect it. But shouldn't this |GHZ> state exist independent of whether we measure all four photons in the |45> basis and detect 4-fold coincidence?
zonde said:
"For entanglement swapping: is entanglement created between photons 2 and 3 when they hit the beam splitter"
No. Besides in this experiment it is explained as creation of entanglement between photons 1 and 4.
"In entanglement swapping 1 and 2 are entangled, and 3 and 4 are entangled. Then 2 and 3 are jointly measured in a particular way. At the end *conditioned on the result of the measurement*, 1 and 4 are entangled. So, indeed, at no time do any of the photons have a definite polarization."
Conditioned on the result of the measurement? So not all the times 2 and 3 are measured (2 and 3 going to separate detectors) will 1 and 4 be entangled? I'm thinking I might have that wrong though... Surely each time you measure 2 and 3 (in whichever basis), it forces them to take on a particular bell-state, and hence 1 and 4 the same bell-state = entanglement each time.