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**'''mixed output case:''' In this case, $P_{succ} = 1$ and the described protocol is perfect. | **'''mixed output case:''' In this case, $P_{succ} = 1$ and the described protocol is perfect. | ||
== | ==Protocol Description== | ||
'''<u>Stage 1</u>''' Preparation and operation</br></br> | '''<u>Stage 1</u>''' Preparation and operation</br></br> | ||
*'''Input:''' The ancillary state <math>|a\rangle = \alpha|1\rangle + \beta |0\rangle</math>, <math>|\psi\rangle</math>, <math>|\psi^\perp\rangle</math> | *'''Input:''' The ancillary state <math>|a\rangle = \alpha|1\rangle + \beta |0\rangle</math>, <math>|\psi\rangle</math>, <math>|\psi^\perp\rangle</math> |