Adaptive quantum homodyne tomography

An adaptive optimization technique to improve the precision of quantum homo dyne tomography is presented. The method is based on the existence of so-ca lled null Functions, which have a zero average for an arbitrary state of ra diation. The addition of null functions to the tomographic kernels does not affect their mean values, but changes statistical errors, which can then b e reduced by an optimization method that "adapts" kernels to homodyne data. Applications to tomography of the density matrix and other relevant field observables are studied in detail. [S1050-2947(99)00707-6].