4.8 Article

Quantum-State Reconstruction by Maximizing Likelihood and Entropy

Journal

PHYSICAL REVIEW LETTERS
Volume 107, Issue 2, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.107.020404

Keywords

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Funding

  1. NUS Graduate School (NGS)
  2. Ministry of Education
  3. National Research Foundation of Singapore
  4. Czech Ministry of Education [MSM6198959213]
  5. Czech Ministry of Industry and Trade [FR-TI1/364]

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Quantum-state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements, as a rule, does 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.

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