In Aspect's paper "Bell's Theorem: The naive..." and in an 2002 AJP article by Dehlinger and Mitchell "Entangled photon apparatus..." the photons are described to be in the $|xx\rangle+|yy\rangle$ state, meaning that the linear polarizations are 100% correlated. Are there 2-photon decay processes where the state contains only $|xy\rangle$ and $|yx\rangle$ kets, meaning that they are 100% anticorrelated?
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1$\begingroup$ Yes; it depends on the process used when they are generated. If the original state has net spin zero, the photons must have opposite spins. $\endgroup$– Peter DiehrCommented Apr 27, 2016 at 23:45
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$\begingroup$ in decays (the title) there is conservation of angular momentum . $\endgroup$– anna vCommented Apr 30, 2016 at 4:52
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I finally figured it out, at least for the simple case where the two atomic states have the same angular momentum: In this case the photons are always opposite in angular momentum (meaning they are either both left or both right handed). Regarding linear polarization, it depends on the parity of the system. In one case the linear polarizations are 100% correlated, and in the other, they are 100% anti-correlated. It's all explained in Feynmann Chapter 18 volume III.