acta physica slovaca

Acta Physica Slovaca 69, No.1, 1 – 74 (2019) (74 pages)


Leonardo Andreta de Castro1 , Olimpio Pereira de Sá Neto2 , Carlos Alexandre Brasil3,4
   1Department of Electrical and Computer Engineering, Duke University, Durham NC, 27708, USA
   2Coordenação de Ciência da Computação, Universidade Estadual do Piaulo, CEP 64202-220, Parnaı́ba, PI, Brazil
   3Department of Physics and Materials Science (FCM), São Carlos Institute of Physics (IFSC), University of São Paulo (USP), PO Box 369, CEP 13560-970, São Carlos, SP, Brazil
   4Departamento Acadêmico de Ciências da Natureza (DACIN), Campus Cornélio Procópio (CP), Universidade Tecnológica Federal do Paraná (UTFPR), Avenida Alberto Carazzai 1640, CEP 86300-000, Cornélio Procópio, PR, Brazil

Full text: ::pdf :: (Received 02 May 2019, accepted 06 August 2019)

Abstract: We provide an introduction to the theory of quantum measurements that is centered on the pivotal role played by John von Neumann’s model. This introduction is accessible to students and researchers from outside the field of foundations of quantum mechanics and presented within a historical context. We first explain the origins and the meaning of the measurement problem in quantum theory, and why it is not present in classical physics. We perform a chronological review of the quantization of action and explain how this led to successive restrictions on what could be measured in atomic phenomena, until the consolidation of the orthodox interpretation of quantum mechanics. The clear separation between quantum system and classical apparatus that causes these restrictions is subverted in von Neumann’s paradigmatic model of quantum measurements, a subject whose concepts we explain, while also providing the mathematical tools necessary to apply it to new problems. We show how this model was important in discussing the interpretations of quantum mechanics and how it is still relevant in modern applications. In particular, we explain in detail how it can be used to describe weak measurements and the surprising results they entail. We also discuss the limitations of von Neumann’s model of measurements, and explain how they can be overcome with POVMs and Kraus operators. We provide the mathematical tools necessary to work with these generalized measurements and to derive master equations from them. Finally, we demonstrate how these can be applied in research problems by calculating the Quantum Zeno Effect.

Keywords: Complementarity principle, von Neumann model of measurements, Weak measurements, Non-projective measurements, Measurement master equations, Quantum Zeno effect
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