Operational tomography: Fitting of data patterns

Abstract

We build an operational scheme for the quantum state reconstruction based on the fitting of data patterns. Each data pattern corresponds to the response of the measurement setup to a predefined reference state. The set of data patterns can be measured experimentally in the calibration stage preceding to the reconstruction. The quorum of reference states plays the role of a positive operator valued measure in terms of which the reconstruction is done. As the main advantage, the procedure is free of notorious problems with projections into non-normalizable quadrature eigenstates, infinite dimensionality, ill-posed inversion, or imperfect detection. © 2010 The American Physical Society.