### Abstract

The photon statistics and, moreover, the density matrix (quantum state) of a single light mode can be sampled using homodyne detection. That is, the density matrix is computed by averaging a set of sampling functions with respect to the measured quadrature values. We develop a practical procedure for evaluating these functions. The algorithm is simple, stable, has small computer-memory requirements, and is last enough for real-time data processing. (Interestingly, our method involves unnormalizable solutions of the stationary Schrödinger equation. We develop the annihilation-and-creation formalism for these solutions and derive their semiclassical approximations.) We quantify the bin width required to determine the density matrix up to a maximal quantum number. Finally, we show how the statistical errors of the reconstructed density matrix can be determined from the measured data.

Original language | English |
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Pages (from-to) | 144-160 |

Number of pages | 17 |

Journal | Optics Communications |

Volume | 127 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Jun 1 1996 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Physical and Theoretical Chemistry
- Electrical and Electronic Engineering

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## Cite this

*Optics Communications*,

*127*(1-3), 144-160. https://doi.org/10.1016/0030-4018(96)00061-2