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Probabilistic Cloning: Difference between revisions
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→Two qubit case
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here we labelled the three qubits by x, y and z</br></br> | here we labelled the three qubits by x, y and z</br></br> | ||
'''<u>Stage 3</u>''' Measurements </br> | '''<u>Stage 3</u>''' Measurements </br> | ||
'''Input:''' <math>\sqrt{p}|\psi_{\pm}\rangle_x|\psi_{\pm}\rangle_y|0\rangle_z + \sqrt{1-p}|\Phi\rangle_{xy}|1\rangle_z</math> | '''Input:''' <math>\sqrt{p}|\psi_{\pm}\rangle_x|\psi_{\pm}\rangle_y|0\rangle_z + \sqrt{1-p}|\Phi\rangle_{xy}|1\rangle_z</math></br> | ||
'''Output:''' <math>|\psi_{\pm}\rangle_x|\psi_{\pm}\rangle_y</math> with probabiliy p | '''Output:''' <math>|\psi_{\pm}\rangle_x|\psi_{\pm}\rangle_y</math> with probabiliy p | ||
# Measure qubit z in the standard basis ( | # Measure qubit z in the standard basis (<math>|0\rangle</math> and <math>|1\rangle</math> basis). | ||
##'''If''' the output of the measurement is <math>|0\rangle</math> | ##'''If''' the output of the measurement is <math>|0\rangle</math> | ||
##'''Then''' the protocol is successful and the final state of the machine are <math>|\psi_{\pm}\rangle_x|\psi_{\pm}\rangle_y</math> | ##'''Then''' the protocol is successful and the final state of the machine are <math>|\psi_{\pm}\rangle_x|\psi_{\pm}\rangle_y</math> | ||
##'''Else''' the protocol failed and the final state of the machine is <math>|\Phi\rangle_{xy}</math> | ##'''Else''' the protocol failed and the final state of the machine is <math>|\Phi\rangle_{xy}</math> | ||
===The quantum circuit=== | ===The quantum circuit=== | ||
Finally, the quantum circuit which illustrates the above stages can be described to consist of following gates and parts which have been also shown in the figure in [[Probabilistic Cloning#Outline|Outline]] | Finally, the quantum circuit which illustrates the above stages can be described to consist of following gates and parts which have been also shown in the figure in [[Probabilistic Cloning#Outline|Outline]] | ||