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I'm taking a quantum information course and one of my exercises says to find $p,p'$, for which there is a channel $\tilde\Lambda(\Lambda(\rho))=\Lambda'(\rho)$, where $\Lambda$ and $\Lambda'$ are dephasing channels with $\Lambda(\rho)=(1-p)\rho+p\sigma_z\rho\sigma_z, \Lambda'(\rho)=(1-p')\rho+p'\sigma_z\rho\sigma_z$. I'm rather confused how to do that, would appreciate any tips and hints.

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    $\begingroup$ It looks as though the two maps are very similar. Have you considered describing them both in terms such as $\Lambda_p(\rho) := (1-p)\rho + p[ \sigma _z \rho \sigma_z] $, and considered what the effect of this map is on the coefficients of the density matrix? $\endgroup$ – Niel de Beaudrap Dec 4 '18 at 17:12
  • $\begingroup$ $\tilde{\Lambda}$ follows similar pattern? $\endgroup$ – AHusain Dec 4 '18 at 19:00

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