# Photon entanglement question

1. Dec 17, 2011

### fulis

A question came up about entanglement and I've only studied very little QM so far, so I went to wikipedia to see if I could become any wiser and they had an example on photon entanglement which was quite straight forward (though the whole page lacks sources =[ ). The example shows that if you have photons going in opposite directions and that are entangled such that they will have the same polarization and their state is a superposition of vertical and horizontal polarization states then they actually don't have a polarization. Kind of a neat result.

Anyway, I figured I'd try to change the example a bit by having the two photons have opposite polarizations instead, so instead of the state:
|1,V>|2,V>+|1,H>|2,H>
I used:
|1,V>|2,H>+|1,H>|2,V>

I did the exact same substitution for the V and H states as they did in the example. I was expecting to get:
|1,45>|2,135>+|1,135>|2,45> since the photons are entangled in such a way that they have opposite polarization, but instead I got (I haven't normalized any of these expressions):
|1,45>|2,45>-|1,135>|2,135>

which is contradictory to the entanglement. The actual calculation is really simple and I did double check it a few times so I'm guessing the problem is something else. It's not exactly the best written wiki entry so I don't trust it to be right :D if someone else could show me how you actually calculate it I'd be grateful

2. Dec 18, 2011

### jrlaguna

You'll have to be more precise... |1V>|2H> + |1H>|2V> seems to me like a perfectly formed quantum state of two photons (modulo normalization, of course). Why do you rotate the local basis?