  Strategies to protect multi-qubit states against decoherence are difficult to
formulate because of their complex many-body dynamics. A better knowledge of
the decay dynamics would help in the construction of decoupling control
schemes. Here we use solid-state nuclear magnetic resonance techniques to
experimentally investigate the decay of coherent multi-spin states in linear
spin chains. Leveraging on the quasi-one-dimensional geometry of Fluorapatite
crystal spin systems, we can gain a deeper insight on the multi-spin states
created by the coherent evolution, and their subsequent decay, than it is
possible in 3D systems. We are then able to formulate an analytical model that
captures the key features of the decay. We can thus compare the decoherence
behavior for different initial states of the spin chain and link their decay
rate to the state characteristics, in particular their coherence and long-range
correlation among spins. Our experimental and theoretical study shows that the
spin chains undergo a rich dynamics, with a slower decay rate than for the 3D
case, and thus might be more amenable to decoupling techniques.
