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Theres a photo on the wikipedia page Quantum Entanglement there's a image of a photon being split into two entangled photons via crystal. I used this picture to demonstrate the scenario below.

Spontaneous parametric down-conversion process can split photons into type II photon pairs with mutually perpendicular polarization.

Below I have a picture of a photon beam getting split into two entangled photons. These entangled photons are being split again to create two 2 sets of entangled photons. Is this possible? Is it possible to create two entangled photos from an already entangled photon?

If this is possible, I'm wondering what the relationship the children of an entangled photon and it's cousins, and the relationship if child to aunt / uncle particle. I'm curious toward the behavior of the spin relation between a family of entangled particles.

Im interested in a notion where all particles in the universe are more hierarchically related then we think.

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  • $\begingroup$ The produced photons haven't enough energy for the crystal to produce again two photons. If one find an other possibility to produce two photons from one photon of this energy, then one will get entangled photons again. $\endgroup$
    – HolgerFiedler
    Aug 28, 2015 at 10:27
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    $\begingroup$ @HolgerFiedler That's absurd. You can move an identical crystal towards the beam at relativistic speed or shoot the photons downwards in a deep gravity well. These might not be cheap or easy but you can't just say something can't be down just because it is harder or more expensive than you wanted it to be. It's a legitimate question. $\endgroup$
    – Timaeus
    Aug 28, 2015 at 15:58
  • $\begingroup$ @HolgerFiedler Yes, assuming that you could generate a photon beam given enough energy to compensate for the dilution of the beam during the splitting stages, and you could produce entangled child particles, my question is: Would there be any relation between child + parent, child + sibling, child + aunt / uncle? $\endgroup$
    – ThomasReggi
    Aug 28, 2015 at 17:10

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Entanglement is a quantum mechanical phenomenon. It is a shorthand to saying " aspects of the wavefunction for these particles are completely known", i.e. the particles are entangled by the wavefunction describing their probabilistic behavior.

A laser beam emerges from zillions of coherent photons, i.e. their phases with respect to each other and the beam are know. The wavefunction describing individual photon contributions may be explored. This is what the description is about.

A photon beam cannot be split into two entangled or not photons as it is composed out of zilions of photons. The beam itself can be split, and because the quantum dynamics solution for a laser beam is known the phases between individual photons may be also known.

It is just stating that a photon from the vertically polarized beam has a counterpart in the horizontally polarized beam. From the zillions of photons there are pairs that are entangled, i.e. if you measure the polarization of one photon you know that there exists another photon with the complimentary polarisation. That is all. No family trees and relationships because it is not the same photon that does the gymnastics .

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