2019/12/20 by Arnold Neumaier, Neumaier, Arnold
Computer Science · Physics and Astronomy · #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Mechanical and Optical Resonators #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #primary: 81P15 #secondary: 81-01
paper · pdf · doi:10.48550/arxiv.1912.09906
openalex publication_date 2019/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Born's rule in its conventional textbook form applies to the small class of projective measurements only. It is well-known that a generalization of Born's rule to realistic experiments must be phrased in terms of positive operator valued measures (POVMs). This generalization accounts for things like losses, imperfect measurements, limited detection accuracy, dark detector counts, and the simultaneous measurement of position and momentum. Starting from first principles, this paper gives a self-contained, deductive introduction to quantum measurement and Born's rule, in its generalized form that applies to the results of measurements described by POVMs. It is based on a suggestive definition of what constitutes a detector, assuming an intuitive informal notion of response. The formal exposition is embedded into the context of a variaety of quotes from the literature illuminating historical aspects of the subject. The material presented suggests a new approach to introductory courses on quantum mechanics.