## 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 that 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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Pages (from-to) | 15 |

Number of pages | 1 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 64 |

Issue number | 5 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics