Quantum capacity for the amplitude damping channel and the pure dephasing channel have closed-form formulas as it can be seen in section 24.7.2 of From Classical to Quantum Shannon Theory. However, I am unsure if there exist such a result for the more complete decoherence model that combines both actions into the combined amplitude and phase damping channel. This is a Kraus rank $3$ quantum channels with the following error operators \begin{equation}\label{eq:ampphaseKraus} \begin{aligned} E_0 &= \begin{pmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma-(1-\gamma)\lambda} \end{pmatrix} \\ \\E_1 &= \begin{pmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{pmatrix} \\E_2 &= \begin{pmatrix} 0 & 0 \\ 0 & \sqrt{(1-\gamma)\lambda} \end{pmatrix} \end{aligned} \end{equation} where $\gamma$ is the damping parameter and $\lambda$ is the scattering parameter. This channel can be seen as the serial composition of the composing ampitude damping channel and dephasing channel as $\mathcal{N}_{\mathrm{APD}}=\mathcal{N}_{\mathrm{PD}}\circ \mathcal{N}_{\mathrm{AD}}$. I am wondering if there is some known result on the capacity of this channel, as it happens for its constituting channels.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.