title: Quantum-state reconstruction by maximizing likelihood and entropy.
abstract: 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.
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore.
authors.forename: Yong Siah
authors.initials: YS
authors.lastname: Teo
authors.forename: Huangjun
authors.initials: H
authors.lastname: Zhu
authors.forename: Berthold-Georg
authors.initials: BG
authors.lastname: Englert
authors.forename: Jaroslav
authors.initials: J
authors.lastname: Řeháček
authors.forename: Zdeněk
authors.initials: Z
authors.lastname: Hradil