Spatially encoded pseudopure states for NMR quantum-information processing

Quantum-information processing by liquid-state NMR spectroscopy uses pseudopure states to mimic the evolution and observations on true pure states. A new method of preparing pseudopure states is described, which involves the selection of spatially labeled states of an ancilla spin with which the spin system of interest is correlated. This permits a general procedure to be given for the preparation of pseudopure states on any number of spins, subject to the limitations imposed by the loss of signal from the selected subensemble. The preparation of a single pseudopure state is demonstrated by carbon and proton NMR of ¹³C-labeled alanine. With a judicious choice of magnetic-field gradients, the method further allows encoding of up to 2N pseudopure states in independent spatial modes in an $N+1$ spin system. Fast encoding and decoding schemes are demonstrated for the preparation of four such spatially labeled pseudopure states.