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State Dependent N-M Cloning: Difference between revisions
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#Perform a unitary on N input states of the form <math>|x\rangle^{\otimes N}</math>, with <math>x = a, b</math> and also on <math>(M-N)</math> blank states, which its action is discribed by:</br> | #Perform a unitary on N input states of the form <math>|x\rangle^{\otimes N}</math>, with <math>x = a, b</math> and also on <math>(M-N)</math> blank states, which its action is discribed by:</br> | ||
<math>|\alpha_{NM}\rangle = U_{NM} (|a\rangle^{\otimes N} \otimes |0\rangle^{\otimes M-N}) = (A + B)|a^M\rangle + (A - B)|b^M\rangle</math>,</br> | <math>|\alpha_{NM}\rangle = U_{NM} (|a\rangle^{\otimes N} \otimes |0\rangle^{\otimes M-N}) = (A + B)|a^M\rangle + (A - B)|b^M\rangle</math>,</br> | ||
<math>|\beta_{NM}\rangle = U_{NM} (|b\rangle^{\otimes N} \otimes |0\rangle^{\otimes M-N}) = (A - B)|a^M\rangle + (A + B)|b^M\rangle</math>, </br> | <math>|\beta_{NM}\rangle = U_{NM} (|b\rangle^{\otimes N} \otimes |0\rangle^{\otimes M-N}) = (A - B)|a^M\rangle + (A + B)|b^M\rangle</math>, </br></br> | ||
where</br> | where,</br> | ||
<math>A = \frac{1}{2}\sqrt{\frac{1 + S^N}{1 + S^M}}, \quad B = \frac{1}{2}\sqrt{\frac{1 - S^N}{1 - S^M}}</math> | <math>A = \frac{1}{2}\sqrt{\frac{1 + S^N}{1 + S^M}}, \quad B = \frac{1}{2}\sqrt{\frac{1 - S^N}{1 - S^M}}</math> | ||
==Further Information== | ==Further Information== | ||
One of the most important applications of quantum cloning is to analyze the security of [[Quantum Key Distribution]] (QKD) protocols. Usually, an eavesdropper is supposed in QKD protocols os assumed to be able to perform any attacks, including copying of states used by parties involved in the protocol. Special states which are being used in different QKD protocols will lead to different state-dependent cloners for analyzing cloning attacks. | One of the most important applications of quantum cloning is to analyze the security of [[Quantum Key Distribution]] (QKD) protocols. Usually, an eavesdropper is supposed in QKD protocols os assumed to be able to perform any attacks, including copying of states used by parties involved in the protocol. Special states which are being used in different QKD protocols will lead to different state-dependent cloners for analyzing cloning attacks. | ||