Entanglement production by quantum error correction in the presence of correlated environment

– We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between physical qubits. We show that for short times the quantum error correction interprets such entanglement as errors and suppresses it. However for longer time, although quantum error correction is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment. Quantum error correction (QEC) [1, 2] has been introduced to perform quantum information processing [3] in the presence of noise due to the interaction between quantum bits and environment. The basic idea is to encode each logical qubit in a redundant way on a set of physical qubits and to periodically acquire information on the errors that affected the system but not on the quantum state of the system itself. Such techniques have been developed to deal with independent errors on individual physical qubits due to the interaction of each physical qubit with its own reservoir. In several physical situations however the presence of correlated reservoirs [4] can result in non-trivial effects. For example it has been shown that the interaction of two subsystems with a finite temperature common bath of harmonic oscillators can, for short times, induce entanglement between the two subsystems initially in a product state. This is possible when the environment has some spatial correlations [5], as often occurs in solid state physics, leading to an effective interaction between the two subsystems. This effect is also present for noisy baths in the Markovian regime [6]. The dynamics of the entanglement rate in the presence of decoherence was also studied [7]. Quantum error correction has been analyzed in the presence of correlated environments in Ref. [8]. In the present work we address the issue of the effects of QEC on the entanglement