Dissipation and decoherence in a quantum register

A model for a quantum register R made of N replicas of a d-dimensional quantum system (cell) coupled with the environment is studied by means of a Born-Markov master equation (ME). Dissipation and decoherence are discussed in various cases in which a subdecoherent encoding can be rigorously found. For the quantum-bit case (d=2) we have solved, for small N, the ME by numerical direct integration and studied, as a function of the coherence length ξ_c of the bath, fidelity and decoherence rates of states of the register. For large enough ξ_c the singlet states of the global su(2) pseudo spin algebra of the register (noiseless at ξ_c=∞) are shown to have a much smaller decoherence rates than the rest of the Hilbert space.