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We investigate the influence of environmental noise on spin networks and spinchains. In addition to the common model of an independent bath for each spin inthe system we also consider noise with a finite spatial correlation length. Wepresent the emergence of new dynamics and decoherence-free subspaces withincreasing correlation length for both dephasing and dissipating environments.This leads to relaxation blocking of one spin by uncoupled surrounding spins.We then consider perfect state transfer through a spin chain in the presence ofdecoherence and discuss the dependence of the transfer quality on spatial noisecorrelation length. We identify qualitatively different features for dephasingand dissipative environments in spin-transfer problems.

Excitation- and state-transfer through spin chains in the presence of spatially correlated noise