Joint Seminar on Quantum Information and Technologies

In this work, we present quantum error correction (QEC) conditions for a system undergoing open-system dynamics. Here, we describe the noise on the system as originating from a joint completely-positive, trace-preserving channel on the system-environment composite, after which we trace out the environmental degree of freedom. Our noise model can be viewed as an intermediate picture between the standard system-only quantum channel model and a system-bath Hamiltonian noise model: It goes beyond a Markovian description for the system dynamics, and yet keeping a quantum dynamical semigroup structure for the problem. Our general noise model fits naturally into many physical scenarios, where one has a relatively strong coupling between the system and an ``intermediate" bath, which also couples weakly to a much larger and dissipative environment. The large dissipative large environment permits an effective quantum dynamical semigroup description on the joint system-intermediate bath composite. Despite the physical motivation from an "intermediate bath", our noise model is however mathematically general, and in turn contains both system-only quantum channel model and system-bath Hamiltonian noise model as special examples. We derive and study the QEC conditions for our general noise model, with the emphasis that the recovery operation acts on the system only. When the noise is only approximately correctable, we obtain a lower bound for the performance of the QEC, as quantified by worst-case fidelity.