Quantum reading of quantum information

We extend the notion of quantum reading to the case where the information to be retrieved, which is encoded into a set of quantum channels, is of quantum nature. We use two-qubit unitaries describing the system-environment interaction, with the initial environment state determining the system's input-output channel and hence the encoded information. The performance of the most relevant two-qubit unitaries is determined with two different approaches: (i) one-shot quantum capacity of the channel arising between environment and system's output; (ii) estimation of parameters characterizing the initial quantum state of the environment. The obtained results are mostly in (qualitative) agreement, with some distinguishing features that include the CNOT unitary.