Quantum mechanics via quantum tomography

Starting from a new basic principle inspired by quantum tomography rather than from Born's rule, this paper gives an elementary, and self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum detector and for the behavior of its responses leads to a logically impeccable definition of measurement. Applications to measurement schemes for optical states, position measurements and particle tracks demonstrate that this definition is applicable to complex realistic experiments without any idealization. The various forms of quantum tomography for quantum states, quantum detectors, quantum processes, and quantum instruments are discussed. The traditional dynamical and spectral properties of quantum mechanics are derived from a continuum limit of quantum processes. In particular, the Schr\"odinger equation for the state vector of a pure, nonmixing quantum system and the Lindblad equation for the density operator of a mixing quantum system are shown to be consequences of the new approach. Normalized density operators are shown to play the role of quantum phase space variables, in complete analogy to the classical phase space variables position and momentum. A slight idealization of the measurement process leads to the notion of quantum fields, whose smeared quantum expectations emerge as reproducible properties of regions of space accessible to measurements. A variety of quotes from the literature illuminate the formal exposition with historical and philosophical aspects.Comment: 91 pages, partially based on my paper arXiv:1912.09906. Compared to v2, an extended overview was added, and the material in Sections 5-7 was partially reworke