1,383 research outputs found
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
Analogy between optimal spin estimation and interferometry
Scheme for optimal spin state estimation is considered in analogy with phase
detection in interferometry. Recently reported coherent measurements yielding
the average fidelity (N+1)/(N+2) for N particle system corresponds to the
standard limit of phase resolution 1/\sqrt{N}. It provides the bound for
incoherent measurements when each particle is detected separately and
information is used optimally. For specific states, improvement up to the value
1/N is possible in quantum theory. The best results are obtained combining
sequentially coherent measurements on fractional groups of particles.Comment: 5 page
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,
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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
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