MaxEnt assisted MaxLik tomography

Maximum likelihood estimation is a valuable tool often applied to inverse problems in quantum theory. Estimation from small data sets can, however, have non unique solutions. We discuss this problem and propose to use Jaynes maximum entropy principle to single out the most unbiased maximum-likelihood guess.Comment: 10 pages, 5 figures, presented at MaxEnt conference in Jackson, WY, 200

Iterative algorithm for reconstruction of entangled states

An iterative algorithm for the reconstruction of an unknown quantum state from the results of incompatible measurements is proposed. It consists of Expectation-Maximization step followed by a unitary transformation of the eigenbasis of the density matrix. The procedure has been applied to the reconstruction of the entangled pair of photons.Comment: 4 pages, no figures, some formulations changed, a minor mistake correcte

Quantum tomography as normalization of incompatible observations

Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations. The proposed approach handles the noisy data corresponding to realistic incomplete observation with finite resolution.Comment: RevTeX, 4 pages, 3 figure

Quantum state estimation

New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not guarantee the positive definiteness of the reconstructed density matrix.Comment: 4 pages, twocolumn Revte

Quantum theory of incompatible observations

Maximum likelihood principle is shown to be the best measure for relating the experimental data with the predictions of quantum theory.Comment: 3 page