Relaxation of pseudo pure states: the role of cross-correlations

In quantum information processing by NMR one of the major challenges is relaxation or decoherence. Often it is found that the equilibrium mixed state of a spin system is not suitable as an initial state for computation and a definite initial state is required to be prepared prior to the computation. As these preferred initial states are non-equilibrium states, they are not stationary and are destroyed with time as the spin system relaxes toward its equilibrium, introducing error in computation. Since it is not possible to cut off the relaxation processes completely, attempts are going on to develop alternate strategies like quantum error correction codes or noiseless subsystems. Here we study the relaxation behavior of various pseudo pure states and analyze the role of cross-terms between different relaxation processes, known as cross-correlation. It is found that while cross-correlations accelerate the relaxation of certain pseudo pure states, they retard that of others.