论文标题
量子系统的零件和复合材料
Parts and Composites of Quantum Systems
论文作者
论文摘要
我们考虑三种用于量子测量的实体。按照一般性的顺序，这些类型是：可观察，工具和测量模型。如果$α$和$β$是实体，我们将定义$α$成为$β$的一部分的含义。这种关系本质上等同于$α$是$β$的函数，在这种情况下，$β$可用于测量$α$。然后，我们使用该概念来定义实体的共存并研究其特性。地图$ \ alphahat $扮演着关键角色，该$将某种类型的实体带到了较低的类型之一。例如，如果$ \ iScript $是一种乐器，则$ \ iscripthat $是可观察到的独特观察$，可通过$ \ iscript $衡量。接下来讨论复合系统。这些是通过将所组合系统希尔伯特空间的张量产品构建的。研究了三种类型的测量及其部分的复合材料。讨论了减少其本地组件的类型。我们还考虑测量的顺序产物。 Lüders，Kraus和Trivial Instruments的具体例子用于说明各种概念。我们仅在本文中考虑有限维系统。
We consider three types of entities for quantum measurements. In order of generality, these types are: observables, instruments and measurement models. If $α$ and $β$ are entities, we define what it means for $α$ to be a part of $β$. This relationship is essentially equivalent to $α$ being a function of $β$ and in this case $β$ can be employed to measure $α$. We then use the concept to define coexistence of entities and study its properties. A crucial role is played by a map $\alphahat$ which takes an entity of a certain type to one of lower type. For example, if $\iscript$ is an instrument, then $\iscripthat$ is the unique observable measured by $\iscript$. Composite systems are discussed next. These are constructed by taking the tensor product of the Hilbert spaces of the systems being combined. Composites of the three types of measurements and their parts are studied. Reductions of types to their local components are discussed. We also consider sequential products of measurements. Specific examples of Lüders, Kraus and trivial instruments are used to illustrate various concepts. We only consider finite-dimensional systems in this article.
