Ensemble quantum-information processing by NMR: Spatially averaged logical labeling technique for creating pseudopure states

A method for creating pseudopure states in NMR is described that combines spatial averaging and logical labeling techniques. This method uses one labeling qubit and any desired pseudopure state of any number of qubits can be created in the subsystem manifolds of the labeling qubit. The method uses a nonselective $\pi /2\mathrm{}$ radio frequency pulse on all the nonlabeling qubits to equalize the populations of all the states within each subsystem, followed by a single transition-selective $\pi$ pulse on one of the transitions of the labeling qubit. The transverse magnetization created during the process is destroyed by a magnetic field gradient pulse, yielding a subsystem pseudopure state. The method is demonstrated experimentally on a system of three qubits.