A1 Refereed original research article in a scientific journal
Complementary Observables in Quantum Mechanics
Authors: Kiukas J, Lahti P, Pellonpaa JP, Ylinen K
Publisher: SPRINGER
Publication year: 2019
Journal: Foundations of Physics
Journal name in source: FOUNDATIONS OF PHYSICS
Journal acronym: FOUND PHYS
Volume: 49
Issue: 6
First page : 506
Last page: 531
Number of pages: 26
ISSN: 0015-9018
eISSN: 1572-9516
DOI: https://doi.org/10.1007/s10701-019-00261-3
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/40799705
Abstract
We review the notion of complementarity of observables in quantum mechanics, as formulated and studied by Paul Busch and his colleagues over the years. In addition, we provide further clarification on the operational meaning of the concept, and present several characterisations of complementaritysome of which newin a unified manner, as a consequence of a basic factorisation lemma for quantum effects. We work out several applications, including the canonical cases of position-momentum, position-energy, number-phase, as well as periodic observables relevant to spatial interferometry. We close the paper with some considerations of complementarity in a noisy setting, focusing especially on the case of convolutions of position and momentum, which was a recurring topic in Paul's work on operational formulation of quantum measurements and central to his philosophy of unsharp reality.
We review the notion of complementarity of observables in quantum mechanics, as formulated and studied by Paul Busch and his colleagues over the years. In addition, we provide further clarification on the operational meaning of the concept, and present several characterisations of complementaritysome of which newin a unified manner, as a consequence of a basic factorisation lemma for quantum effects. We work out several applications, including the canonical cases of position-momentum, position-energy, number-phase, as well as periodic observables relevant to spatial interferometry. We close the paper with some considerations of complementarity in a noisy setting, focusing especially on the case of convolutions of position and momentum, which was a recurring topic in Paul's work on operational formulation of quantum measurements and central to his philosophy of unsharp reality.
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