Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization and noiseless measurements   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 $f:\R^2\to \R$ 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 well-known
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 notice that
the noiseless measurements are the ones 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 $\Gamma(f^k)$, $k\in \N$, with
$\Gamma$ a fixed map from classical variables to Hilbert space operators. In
particular, we consider the quantization of classical \emph{questions}, that
is, functions $f:\R^2\to\R$ taking only values 0 and 1. We compare two concrete
realizations of the map $\Gamma$ in view of their ability to produce noiseless
measurements: one being the Weyl map, and the other defined by using phase
space probability distributions.

16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs