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Optimal Universal N-M Cloning: Difference between revisions
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(Created page with " == Functionality Description== Universal <math>N \rightarrow M</math> quantum cloning machine (QCM), transformation acting on N original qubits, $(M - N)$ blank qubits and a...") |
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# Perform the following unitary transformation on input state <math>|N\psi\rangle = |\psi\rangle^{\otimes N} |0\rangle^{\otimes M - N} |R\rangle</math> | # Perform the following unitary transformation on input state <math>|N\psi\rangle = |\psi\rangle^{\otimes N} |0\rangle^{\otimes M - N} |R\rangle</math> | ||
<math>U_{N,M} |N\psi\rangle = \sum_{j=0}^{M-N} \alpha_{j} |(M - j)\psi, j\psi^{\perp}\rangle \otimes R_{j}(\psi)</math></br> | <math>U_{N,M} |N\psi\rangle = \sum_{j=0}^{M-N} \alpha_{j} |(M - j)\psi, j\psi^{\perp}\rangle \otimes R_{j}(\psi)</math></br> | ||
where <math>\alpha_{j} = \sqrt{\frac{N + 1}{M + 1}} \sqrt{\frac{(M - N)!(M - j)!}{(M - N - j)! M!}}</br> | where <math>\alpha_{j} = \sqrt{\frac{N + 1}{M + 1}} \sqrt{\frac{(M - N)!(M - j)!}{(M - N - j)! M!}}</math></br> | ||
<u>'''Stage 3:'''</u> Trace out the QCM state | <u>'''Stage 3:'''</u> Trace out the QCM state | ||
#Trace out the state of the QCM | #Trace out the state of the QCM in <math>R_{j}</math> states. | ||
==Relevant Papers== | ==Relevant Papers== | ||