Quantum capacity for a compound channel with memory
We study a quantum compound Markov chain memory channel, addressing a specific two-state
case, combining an amplitude damping channel and a dephasing channel. The sender's knowledge of this channel
affects the behavior of its coherent information. We study the quantum capacity
of this channel, comparing the case in which transmitter doesn't have any information about the channel
in the current use and the case of an informed user.
This is done by maximizing coherent information respect to the input of amplitude damping channel
and depolarizing channel.
We also propose a Hamiltonian for this channel which well describes our model in certain
limit conditions, thus substantiating it from the physical point of view. Moreover the
Hamiltonian model allows for generalization of the compound channel.
This work offers a practical and suitable for applications case-study which demonstrates
that uninformed user case represents the "worse case" scenario.