Point Estimation of States of Finite Quantum Systems

Details Point Estimation of States of Finite Quantum Systems Point Estimation of States of Finite Quantum Systems

2006-10-16

arxiv.org/abs/quant-ph/0610124v1

Physics

Quantum Physics

16 pages, 5 figures

Scientific paper

10.1088/1751-8113/40/28/S06

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the properties of the estimation procedure depend very much on the invertibility of the true state. In particular, in case of a pure state the estimation is less efficient. Moreover, several estimation schemes are compared for the unknown state of a qubit when one copy is measured at a time. It is shown that the average mean quadratic error matrix is the smallest if the applied observables are complementary. The results are illustrated by computer simulations.

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