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We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error-correcting code. In the limit of continuous error correction we introduce a Markovian master equation that includes the effects of: (a) Hamiltonian evolution; (b) errors caused by the interaction with an environment; and (c) error-correcting operations. The master equation is formally presented for all stabilizer codes and its solution is analysed for the simplest such code.
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Paz et al. (1998) studied this question.
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