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.
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arXiv subjects
J. Summhammer
Publications and source records attributed to J. Summhammer.
Reconstruction of the spin state
System of 1/2 spin particles is observed repeatedly using Stern-Gerlach apparatuses with rotated orientations. Synthesis of such non-commuting observables is analyzed using maximum likelihood estimation as an example of quantum state reconstruction. Repeated incompatible observations represent a new generalized measurement. This idealized scheme will serve for analysis of future experiments in neutron and quantum optics.
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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.
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Interaction-Free Preparation
We demonstrate that the preparation of a very well localized atom beam is possible without physical interaction. The preparation is based on the selection of an adequate ensemble of atoms of an originally wide beam by means of information obtained with a neutron interferometer. In such a case the uncertainty relation can no longer be interpreted as a by-product of the interaction between the system and the preparation apparatus.
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