  We experimentally demonstrate the efficacy of a three-layer nested Uhrig
dynamical decoupling (NUDD) sequence to preserve arbitrary quantum states in a
two-dimensional subspace of the four-dimensional two-qubit Hilbert space, on an
NMR quantum information processor. The effect of the state preservation is
studied first on four known states, including two product states and two
maximally entangled Bell states. Next, to evaluate the preservation capacity of
the NUDD scheme, we apply it to eight randomly generated states in the
subspace. Although, the preservation of different states varies, the scheme on
the average performs very well. The complete tomographs of the states at
different time points are used to compute fidelity. State fidelities using NUDD
protection are compared with those obtained without using any protection. The
nested pulse schemes are complex in nature and require careful experimental
implementation.
