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 ξc of the bath, fidelity and decoherence rates of states of the register. For large enough ξc the singlet states of the global su(2) pseudo spin algebra of the register (noiseless at ξc=∞) are shown to have a much smaller decoherence rates than the rest of the Hilbert space.