Quantization and noiseless measurements

J. Kiukas*, P. Lahti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)

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 : ℝ2 → ℝ is associated with a unique positive operator measure (POM) Ef , 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 Ef in our quantization is defined through its moment operators, which are required to be of the form ⌈(fk), 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 : ℝ2 → 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 languageEnglish
Pages (from-to)2083-2091
Number of pages9
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
Issue number9
DOIs
Publication statusPublished - 14 Feb 2007
Externally publishedYes

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