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Postprocessing of quantum instruments
Physical Review A ( IF 2.9 ) Pub Date : 2021-02-25 , DOI: 10.1103/physreva.103.022615
Leevi Leppäjärvi , Michal Sedlák

Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the concatenation of quantum instruments into a sequence of a certain length. In general, the choice of instrument at any given step in the sequence can be conditionally chosen based on the classical results of all preceding instruments. For two instruments in a sequence we consider the conditional second instrument as an effective way of postprocessing the first instrument into a new one. This is similar to how a measurement described by a positive operator-valued measure (POVM) can be postprocessed into another by way of classical randomization of its outcomes using a stochastic matrix. In this work we study the postprocessing relation of instruments and the partial order it induces on their equivalence classes. We characterize the greatest and the least element of this order, give examples of postprocessings between different types of instruments, and draw connections between postprocessings of some of these instruments and their induced POVMs.

中文翻译:

量子仪器的后处理

研究顺序测量对于量子理论的基础方面和量子技术的实际实现都至关重要,而这两种应用都是通过将量子仪器串联成一定长度的序列来抽象描述的。通常,可以基于所有先前仪器的经典结果,有条件地选择序列中任何给定步骤的仪器选择。对于序列中的两个工具,我们认为有条件的第二个工具是将第一个工具后处理为新工具的有效方法。这类似于通过使用随机矩阵对其结果进行经典随机化的方式,可以将由正运算符值的度量(POVM)描述的度量后处理为另一度量。在这项工作中,我们研究了乐器的后处理关系及其在等价类中引起的偏序。我们描述了此顺序的最大和最小元素,给出了不同类型的仪器之间的后处理示例,并绘制了其中一些仪器的后处理与它们诱导的POVM之间的联系。
更新日期:2021-02-25
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