Effects of imperfect noise correlations on decoherence-free subsystems: SU(2) diffusion model
We present a model of an N-qubit channel where consecutive qubits experience correlated random rotations. Our model is an extension to the standard decoherence-free subsystems approach (DFS) which assumes that all the qubits experience the same disturbance. The variation of rotations acting on consecutive qubits is modeled as diffusion on the SU(2) group. The model may be applied to spins traveling in a varying magnetic field, or to photons passing through a fiber whose birefringence fluctuates over the time separation between photons. We derive an explicit formula describing the action of the channel on an arbitrary N-qubit state. For N=3 we investigate the effects of diffusion on both classical and quantum capacity of the channel. We observe that nonorthogonal states are necessary to achieve the optimal classical capacity. Furthermore we find the threshold for the diffusion parameter above which coherent information of the channel vanishes.