## Abstract

In accordance with the fact that quantum measurements are described in terms of positive operator measures (POMs), we consider certain aspects of a quantization scheme in which a classical variable f : ℝ^{2} → ℝ is associated with a unique positive operator measure (POM) E^{f} , which is not necessarily projection valued. The motivation for such a scheme comes from the wellknown fact that due to the noise in a quantum measurement, the resulting outcome distribution is given by a POM and cannot, in general, be described in terms of a traditional observable, a selfadjoint operator. Accordingly, we note that the noiseless measurements are those which are determined by a selfadjoint operator. The POM E^{f} in our quantization is defined through its moment operators, which are required to be of the form ⌈(f^{k}), k ε ℕ, with ⌈ being a fixed map from classical variables to Hilbert space operators. In particular, we consider the quantization of classical questions, that is, functions f : ℝ^{2} → ℝ taking only values 0 and 1. We compare two concrete realizations of the map ⌈ in view of their ability to produce noiseless measurements: one being the Weyl map, and the other defined by using phase space probability distributions.

Original language | English |
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Pages (from-to) | 2083-2091 |

Number of pages | 9 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 40 |

Issue number | 9 |

DOIs | |

Publication status | Published - 14 Feb 2007 |

Externally published | Yes |