论文标题
非扰动量子测量模型
Nondisturbing Quantum Measurement Models
论文作者
论文摘要
测量模型是描述量子测量过程的框架。在本文中，我们将注意力限制在有限维的希尔伯特空间上的$ mm $ s。假设我们要测量一个可观察的$ a $，其结果$ a_x $由Hilbert Space $ h $的正运营商（效果）表示。我们将$ h $称为基本或对象系统。我们通过量子通道在另一个Hilbert Space $ K $上与探针系统进行$ H $的交互。探针系统包含一个可观察到的探针（或仪表或指针）可观察到的$ f $，其结果$ f_x $是由经常（但不需要）经典的设备测量的。 $ mm $ $协议提供了一种方法，用于确定结果$ h $的结果$ a_x $在结果$ f_x $方面的概率。相互作用渠道通常会以$ k $的初始探针状态纠缠这一状态，这可能很复杂。但是，如果在我们描述的某种意义上不扰动该频道，那么纠缠将大大简化。在本文中，我们为可观察到的公式提供了通过非扰动$ mm $ s来衡量的。我们从相对于量子上下文的非扰动操作员进行的一般讨论开始。我们提出了两个例子，这些例子用单一的非扰动渠道来说明这一理论。
A measurement model is a framework that describes a quantum measurement process. In this article we restrict attention to $MM$s on finite-dimensional Hilbert spaces. Suppose we want to measure an observable $A$ whose outcomes $A_x$ are represented by positive operators (effects) on a Hilbert Space $H$. We call $H$ the base or object system. We interact $H$ with a probe system on another Hilbert space $K$ by means of a quantum channel. The probe system contains a probe (or meter or pointer) observable $F$ whose outcomes $F_x$ are measured by an apparatus that is frequently (but need not be) classical in practice. The $MM$ protocol gives a method for determining the probability of an outcome $A_x$ for any state of $H$ in terms of the outcome $F_x$. The interaction channel usually entangles this state with an initial probe state of $K$ that can be quite complicated. However, if the channel is nondisturbing in a sense that we describe, then the entanglement is considerably simplified. In this article, we give formulas for observables and instruments measured by nondisturbing $MM$s. We begin with a general discussion of nondisturbing operators relative to a quantum context. We present two examples that illustrate this theory in terms of unitary nondisturbing channels.
