Maps for general open quantum systems and a theory of linear quantum error correction

Understand

We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state.

• Since the theory of quantum error correction was developed based on the assumption of completely positive (CP) maps, we present a generalized theory of linear quantum error correction, which applies to any linear map describing the open system evolution.
• In the physically relevant setting of Hermitian maps, we show that the CP-map based version of quantum error correction theory applies without modifications.
• However, we show that a more general scenario is also possible, where the recovery map is Hermitian but not CP.