# Dephasing channels

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.

• 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? – Niel de Beaudrap Dec 4 '18 at 17:12
• $\tilde{\Lambda}$ follows similar pattern? – AHusain Dec 4 '18 at 19:00