- #1
ljagerman
- 16
- 2
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!
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!