From: Hal Finney (hal@finney.org)
Date: Thu Sep 19 2002 - 23:33:47 MDT
Regarding Serafino's explanation of quantum teleportation:
> The complete state of particles 1, 2 and 3 has the form
> |1&2&3> = a |+,1>|+,2>|-,3> - a |+,1>|-,2>|+,3> +
> b |-,1>|+,2>|-,3> - b |-,1>|-,2>|+,3>
> which can also be written as
> |1,2, one> * (-a |+,3> - b |-,3>) +
> |1,2, two> * (-a |+,3> + b |-,3>) +
> |1,2,three> * (a |-,3> + b |+,3>) +
> |1,2, four> * (a |-,3> - b |+,3>)
I think the idea is that "one", "two", "three" and "four" represent the
four possible outcomes of a joint measurement on particles 1 and 2. Based
on some other references, these are of the form (ignoring constants):
|1,2, one> = |+,1>|-,2> - |-,1>|+,2>
|1,2, two> = |+,1>|-,2> + |-,1>|+,2>
|1,2, three> = |+,1>|+,2> - |-,1>|-,2>
|1,2, four> = |+,1>|+,2> + |-,1>|-,2>
I think that works out algebraically.
In the MWI sense this measurement splits the world along the lines above,
so that Bob's remote photon 3 ends up in one of those four states in each
of the four different newly-separated "worlds". Serafino points out that
in one of the worlds this means that Bob ends up with a copy of photon 1
seemingly at the instant the measurement is made.
Hal
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