269 research outputs found
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
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