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If we start with a Bell state

1/Sqrt(2)(|00>+|11>)

and (after moving the second qbit a significant distance away) apply the interferometer transformation

|0> -> 0.5(|0>+|1>)

|1> -> 0.5(|0>-|1>)

to the first qbit, we get

0.5/Sqrt(2)((|0>+|1>)|0>+(|0>-|1>)|1>)

=0.5/Sqrt(2)(|00>+|10>+|01>-|11>)

which gives equal probability of the first qbit ending up in |0> or |1>

Lets now start again with the same spatially separated Bell state but first apply the transformation

|0> -> 0.5(|0>+|1>)

|1> -> 0.5(|0>+|1>)

to the second qbit:

0.5/Sqrt(2)(|0>(|0>+|1>)+|1>(|0>+|1>))

=0.5/Sqrt(2)(|00>+|01>+|10>+|11>)

then apply the original (interferometer) transformation to the first qbit:

0.25/Sqrt(2)((|0>+|1>)|0>+(|0>+|1>)|1>+(|0>-|1>)|0>+(|0>-|1>)|1>)

=0.25/Sqrt(2)(|00>+|10>+|01>+|11>+|00>-|10>+|01>-|11>)

=0.5/Sqrt(2)(|00>+|01>)

Now, the first qbit is in state |0> with 100% (as opposed to 50%) probability as a result of what was done to the second one.

So...can anyone tell me if I made any false assumptions or stupid math mistakes here?

Dustin Soodak

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# A variation of the Bell experiment

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