We provide an introduction to the theory of quantum measurements that is centered on the pivotalrole played by John von Neumann’s model. This introduction is accessible to students andresearchers from outside the field of foundations of quantum mechanics and presented withina historical context. We first explain the origins and the meaning of the measurement problemin quantum theory, and why it is not present in classical physics. We perform a chronologicalreview of the quantization of action and explain how this led to successive restrictions onwhat could be measured in atomic phenomena, until the consolidation of the orthodox interpretationof quantum mechanics. The clear separation between quantum system and classicalapparatus that causes these restrictions is subverted in von Neumann’s paradigmatic modelof quantum measurements, a subject whose concepts we explain, while also providing themathematical tools necessary to apply it to new problems. We show how this model was importantin discussing the interpretations of quantum mechanics and how it is still relevant inmodern applications. In particular, we explain in detail how it can be used to describe weakmeasurements and the surprising results they entail. We also discuss the limitations of vonNeumann’s model of measurements, and explain how they can be overcome with POVMs andKraus operators. We provide the mathematical tools necessary to work with these generalizedmeasurements and to derive master equations from them. Finally, we demonstrate how thesecan be applied in research problems by calculating the Quantum Zeno Effect.

Leonardo Andreta de Castro

Olímpio Pereira de Sá Neto

Carlos Alexandre Brasil

Acta Physica Slovaca Reviews and Tutorials

ACTA PHYSICA SLOVACA 是国际公认的物理学期刊，最初成立于 1950 年。自 1998 年以来被列入 CURRENT CONTENTS。自 2006 年以来，ACTA PHYSICA SLOVACA 发表评论和教程文章。由特定领域的专家撰写的论文旨在让非专家和博士生也可以访问。虽然该期刊有印刷版，但所有期刊都可以从期刊网页免费下载。我们希望新一期的ACTA PHYSICA SLOVACA 对读者有用和有趣。

Acta Physica Slovaca is an internationally recognized physics journal that was established in 1950. Since 1998, it has been included in CURRENT CONTENTS. Starting in 2006, Acta Physica Slovaca has published commentary and tutorial articles. These papers are written by experts in specific fields, aiming to make the content accessible to non-experts and PhD students. While the journal has a print version, all issues are available for free download from the journal's website. We hope that the new issue of Acta Physica Slovaca will be useful and interesting to readers.

《Acta Physica Slovaca》是一本国际公认的物理学期刊，成立于1950年。自1998年起，该期刊被纳入CURRENT CONTENTS。自2006年起，《Acta Physica Slovaca》开始发表评论和教程文章。这些论文由特定领域的专家撰写，旨在使非专家和博士生也能轻松理解。虽然该期刊有印刷版，但所有期刊内容均可从期刊网站免费下载。我们希望新一期的《Acta Physica Slovaca》能为读者提供有用和有趣的内容。

1. AN INTRODUCTION TO QUANTUM MEASUREMENTS WITH A HISTORICAL MOTIVATION

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