### Abstract

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 the case of a pure state, the estimation should be constrained to ensure the positive definiteness of the estimate. An efficient constraining algorithm is proposed and it yields an asymptotically unbiased estimate. 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. All the results are illustrated by computer simulations.

Original language | English |
---|---|

Article number | S06 |

Pages (from-to) | 7955-7969 |

Number of pages | 15 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 40 |

Issue number | 28 |

DOIs | |

Publication status | Published - Jul 13 2007 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Point estimation of states of finite quantum systems'. Together they form a unique fingerprint.

## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*40*(28), 7955-7969. [S06]. https://doi.org/10.1088/1751-8113/40/28/S06