Quantum Process Tomography via L1-norm Minimization
Robert L. Kosut, Quantum Process Tomography via L1-norm Minimization, arXiv:0812.4323v1 [quant-ph], 12/23/2008.
For an initially well designed but imperfect quantum information system, the process matrix is almost sparse in an appropriate basis. Existing theory and associated computational methods (L1-norm minimization) for reconstructing sparse signals establish conditions under which the sparse signal can be perfectly reconstructed from a very limited number of measurements (resources). Although a direct extension to quantum process tomography of the L1-norm minimization theory has not yet emerged, the numerical examples presented here, which apply L1-norm minimization to quantum process tomography, show a significant reduction in resources to achieve a desired estimation accuracy over existing methods.