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Phase Co-variant Cloning: Difference between revisions
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→Phase-covariant cloning with ancilla
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'''<u>Stage 1</u>''' Cloner state preparation | '''<u>Stage 1</u>''' Cloner state preparation | ||
# Prepare a Bell state <math>|\Phi^{+}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math> | # Prepare a Bell state <math>|\Phi^{+}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math> | ||
'''<u> | '''<u>Stage 2</u>''' Cloner transformation</br> | ||
'''Input:''' <math>|\psi(\phi)\rangle_{A}|\Phi^{+}\rangle_{BM}</math></br> | '''Input:''' <math>|\psi(\phi)\rangle_{A}|\Phi^{+}\rangle_{BM}</math></br> | ||
'''Output:''' <math>U_{pca}|\psi(\phi)\rangle_{A}|\Phi^{+}\rangle_{BM}</math></br> | '''Output:''' <math>U_{pca}|\psi(\phi)\rangle_{A}|\Phi^{+}\rangle_{BM}</math></br> | ||
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<math>U_{pca}|1\rangle|0\rangle|0\rangle = (cos\eta|1\rangle|0\rangle + sin\eta|0\rangle|1\rangle)|0\rangle</math></br> | <math>U_{pca}|1\rangle|0\rangle|0\rangle = (cos\eta|1\rangle|0\rangle + sin\eta|0\rangle|1\rangle)|0\rangle</math></br> | ||
<math>U_{pca}|0\rangle|1\rangle|1\rangle = (cos\eta|0\rangle|1\rangle + sin\eta|1\rangle|0\rangle)|1\rangle</math></br> | <math>U_{pca}|0\rangle|1\rangle|1\rangle = (cos\eta|0\rangle|1\rangle + sin\eta|1\rangle|0\rangle)|1\rangle</math></br> | ||
<math>U_{pca}|1\rangle|1\rangle|1\rangle = |1\rangle|1\rangle|1\rangle</math></br> | <math>U_{pca}|1\rangle|1\rangle|1\rangle = |1\rangle|1\rangle|1\rangle</math></br></br> | ||
'''<u>Stage 3</u>''' Discarding ancillary state | '''<u>Stage 3</u>''' Discarding ancillary state | ||
# Discard the extra state. mathematically, trace out the ancilla | # Discard the extra state. mathematically, trace out the ancilla | ||