Incoherence in the controlled Hamiltonian is an important limitation on theprecision of coherent control in quantum information processing. Incoherencecan typically be modelled as a distribution of unitary processes arising fromslowly varying experimental parameters. We show how it introduces artifacts inquantum process tomography and we explain how the resulting estimate of thesuperoperator may not be completely positive. We then go on to attack theinverse problem of extracting an effective distribution of unitaries thatcharacterizes the incoherence via a perturbation theory analysis of thesuperoperator eigenvalue spectra.
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