Laser Beam through Calcite crystal = Photon Entanglement?

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SUMMARY

Shining a laser beam through a calcite crystal results in the splitting of the beam due to the crystal's birefringent properties. While some photons produced through this process may be entangled, the occurrence is rare, with estimates suggesting only one entangled pair per 10^12 photons. The discussion highlights the importance of understanding down conversion in this context, as well as the role of birefringence in photon behavior.

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If I shine a laser beam through a calcite crystal, the beam is split in two, as shown below. Are the photons in the split beams in an entangled state?
DSC_1475 Red laser through calcite crystal.jpg
 
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If that type of crystal performs a down conversion then some of the pairs of photons produced will be entangled but not many, like 1 pair in 10^12 maybe. I'll let an expert comment.
 

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