- #1
dsoodak
- 24
- 0
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