# Polarization coincidence formula for known polarization?

1. Jun 6, 2014

### georgir

Two entangled photons from a same-polarization source have their polarization measured at 120 deg difference from each other. If I understood right all the simplified Bell-theorem and Bell-test explanations out there, QM and experiments say the chance for coincidence will be 25% no matter which two measuring angles we select, as long as they are 120deg from each other.

Now what if both photons are known to have passed through an initial polarizer at 0 deg before we measure?
Are the two photons still entangled, i.e. if we measure both at the same angle (but not necessarily the 0 deg of the initial polarizer) are they still guaranteed to coincide?
And if we measure them at different angles, do we get any "spooky action" relationship between them?

Or do we just get two independent known-polarization photons?

If we measure them at 120 deg and 240 deg, do we get the classically explainable 25%*25% + 75%*75% = 62% chance of coincidence? I guess this is a particularly stupid question as any other coincidence will be completely impossible and break reality and the world will end :p But I just want to make sure...

[EDIT: I might have incorrectly doubled all the measurement angles... oops.]

2. Jun 6, 2014

### DrChinese

1. This is good.

2. Once either polarization entangled photon is measured at 0 degrees, subsequent results will be as if they are both at 0 degrees and they are independent. So product state statistics result.

3. Something like this, yes. Classical odds.

A minor detail you may already know: it is possible for a pair of photons to be entangled but not on the polarization basis. That could occur in your example 2.