Distinguishing quantum measurements of observables in terms of state transformers
Fedor Herbut
备注：
13 pages, Latex2e. Written for the Am. J. Phys.; after three resubmissions, when both referees were satisfied,it was rejected. It is put on the web to do justice to the great efforts of the referees and the author
The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus representation). In this framework the known kinds of measurements of ordinary (as distinct from generalized) observables are distinguished by necessary and sufficient conditions. Thus, repeatable,nonrepeatable, and ideal measurements are characterized both algebraically and geometrically in terms of polar factors of state transformers.
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University of Pavia（帕维亚大学）；Indian Institute of Technology Bhilai（贝利特印度理工学院）；University of Alabama（阿拉巴马大学）；University of Kansas（堪萨斯大学）；Technische Universität München（慕尼黑工业大学）；University of Florida（佛罗里达大学）
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Institute of Theoretical and Applied Informatics, Polish Academy of Sciences（波兰科学院理论与应用信息研究所）；University of Maryland, College Park, Department of Civil and Environmental Engineering（马里兰大学学院市分校土木与环境工程系）
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Quantum coherence is a critical resource for many operational tasks. Understanding how to quantify and manipulate it also promises to have applications for a diverse set of problems in theoretical physics. For certain applications, however, one requires coherence between the eigenspaces of specific physical observables, such as energy, angular momentum, or photon number, and it makes a difference which eigenspaces appear in the superposition. For others, there is a preferred set of subspaces relative to which coherence is deemed a resource, but it is irrelevant which of the subspaces appear in…
