  Quantum information processing by liquid-state NMR spectroscopy uses
pseudo-pure states to mimic the evolution and observations on true pure states.
A new method of preparing pseudo-pure states is described, which involves the
selection of the 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 pseudo-pure 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 pseudo-pure state is demonstrated by carbon and
proton NMR on 13C-labeled alanine. With a judicious choice of magnetic field
gradients, the method further allows encoding of up to 2^N pseudo-pure 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
pseudo-pure states.
