### Abstract

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (“qubits”). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices which are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

Original language | English (US) |
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Title of host publication | Asymptotic Theory of Quantum Statistical Inference |

Subtitle of host publication | Selected Papers |

Publisher | World Scientific Publishing Co. |

Pages | 509-538 |

Number of pages | 30 |

ISBN (Electronic) | 9789812563071 |

ISBN (Print) | 9812560157, 9789812560155 |

DOIs | |

State | Published - Jan 1 2005 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Asymptotic Theory of Quantum Statistical Inference: Selected Papers*(pp. 509-538). World Scientific Publishing Co.. https://doi.org/10.1142/9789812563071_0035