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by ljagerman
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ljagerman
#1
Feb23-12, 09:55 PM
P: 1
My first use of Physics Forums.
I have a question not addressed so far, as far as I can tell.
It's in the area of quantum math for entangled state.

But I cannot figure out how to ask it!
Is there a "new thread" or "new question" tab anyplace?
Is there a menu item for new threads or new questions? If so, where.

In case this is the place, here is my question.
Interested in recent tests of quantum nonlocality in 3-photon GHZ entanglement.
Looking at key paper by Pan, Bouwmeester, Daniell, Weinfurter & Zeilinger in Nature, 403, 2 Feb 2000, p. 515-518.
Key equation is for entangled 3-photon GHZ state; their equation (1):
|Ψ⟩=1/√2 〖(|H⟩〗_1 |H⟩_2 |H⟩_3+|V⟩_1 |V⟩_2 |V⟩_3); no problem here.
Then the experiments introduce optical devices to rotate polarization and induce circlual polarization; equations here are (their (2) and (3):
Pair (2): |H/⟩ =1/√2 |H⟩+|V⟩) and |V/⟩ =1/√2 |H⟩+|V⟩)
Pair (3): |ʘR⟩ =1/√2 |H⟩+i|V⟩) and |ʘL⟩ =1/√2 |H⟩-i|V⟩)
This looks like simple vector trig in a unit circle.
Now they solve (1) above with (2) and (3), and they arrive at their equation (4):
|Ψ⟩=1/2 〖(|ʘR⟩〗_1 |ʘL⟩_2 |H/⟩_3+|ʘL⟩_1 |ʘR⟩_2 |H/⟩_3 +|ʘR⟩_1 |ʘR⟩_2 |V/⟩_3+|ʘL⟩_1 |ʘL⟩_2 |V/⟩_3).
My question: How did they get to (4)? What vector-algebraic (?) steps did they use?
I know a little about Dirac notation, wave functions, etc, but not enough to see how equation (4) was derived.
Please help if you can!

Thanks!
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Greg Bernhardt
#2
Feb23-12, 09:59 PM
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It's the same process in every forum. You found how to do it in the Feedback forum. Replicate that process in another.
ljagerman
#3
Feb23-12, 10:15 PM
P: 1
Got it: So now it's in 2 places, but I guess not harm. Please see in Physics, Quantum mech. area


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