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StevieTNZ
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Hi there
I'm reading through Valerio Scarani's "Six Quantum Pieces" and have hit an exercise which requires verification of an equality.
where the letters in the brackets indicate the photons.
How does one verify the above equality. The answer given in the book is
That is where I am stuck. I know the different bell-states, but entangle swapping photons that are entangled differently I can't figure out what the outcomes will be.
Any help much appreciated
Stevie
I'm reading through Valerio Scarani's "Six Quantum Pieces" and have hit an exercise which requires verification of an equality.
Suppose that photons D-A, B-C are entangled as follows:
photons D and A: Psi+ = 1/2 |H>|V> + |V>|H>
photons B and C: Phi+ = 1/2 |H>|H> + |V>|V>
Verify the following equality
Psi+(DA)Phi+(BC) = Phi+(AB)Psi+(CD) + Phi-(AB)Psi-(CD) + Psi+(AB)Phi+(CD) + Psi-(AB)Phi-(CD)
where the letters in the brackets indicate the photons.
How does one verify the above equality. The answer given in the book is
Expand the left side:
|H>|V>|H>|V> + |V>|H>|H>|H> + |H>|V>|V>|V> + |V>|H>|V>|V>
Next, using the definitions of the Bell bases in an equation, similarly expand and simplify the expression above to verify the equality.
That is where I am stuck. I know the different bell-states, but entangle swapping photons that are entangled differently I can't figure out what the outcomes will be.
Any help much appreciated
Stevie