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arXiv quant-ph/0612054quant-ph
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量化和无噪声测量

Quantization and noiseless measurements

J. Kiukas, P. Lahti

备注：
15 pages, submitted to Journal of Physics A
发表信息：
J. Phys. A: Math. Theor. 40 (2007) 2083-2091
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摘要：

根据这一事实，量子测量描述的积极运营商措施（POM），我们认为某些方面的量化方案，其中一个经典的变量$f:\R^2\to \R$是与一个独特的积极运营商措施（POM）$E^f$，这不一定是投影值。这种方案的动机来自于众所周知的事实，即由于量子测量中的噪声，所得到的结果分布由POM给出，并且通常不能用传统的可观测量（自伴算子）来描述。因此，我们注意到，无噪声测量是由自伴算子确定的。在我们的量子化中，POM $E^f$是通过其矩算子定义的，这些矩算子需要具有$Γ(f^k)$，$k\in \N$的形式，其中$Γ$是从经典变量到希尔伯特空间算子的固定映射。特别是，我们考虑的经典\emph{questions}，即，功能$f:\R^2\to\R$只取值0和1的量化。我们比较了两个具体的实现的地图$Γ$鉴于他们的能力，以产生无噪声的测量：一个是Weyl地图，和其他定义使用相空间概率分布。

英文摘要：

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 $Γ(f^k)$, $k\in \N$, with $Γ$ 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 $Γ$ in view of their ability to produce noiseless measurements: one being the Weyl map, and the other defined by using phase space probability distributions.

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