Knowledge and ignorance in incomplete quantum state tomography
arXiv:1102.2662 · doi:10.1103/PhysRevLett.107.020404
Abstract
Quantum state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements does, as a rule, not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is the least-bias estimator, consistent with a given set of measurement data. This is equivalent to the joint consideration of our partial knowledge and ignorance about the ensemble to reconstruct its identity. An interesting structure of such estimators will also be explored.
5 pages, 2 figures
References in corpus (4)
- Generation of a superposition of odd photon number states for quantum information networks
- Quantum homodyne tomography of a two-photon Fock state
- Diluted maximum-likelihood algorithm for quantum tomography
- A two-step MaxLik-MaxEnt strategy to infer photon distribution from on/off measurement at low quantum efficiency
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