Positive-operator-valued measures in the Hamiltonian formulation of quantum mechanics

D. Arsenović, N. Burić, D. B. Popović, M. Radonjić, and S. Prvanović
Phys. Rev. A 91, 062114 – Published 12 June 2015

Abstract

In the Hilbert space formulation of quantum mechanics, ideal measurements of physical variables are discussed using the spectral theory of Hermitian operators and the corresponding projector-valued measures (PVMs). However, more general types of measurements require the treatment in terms of positive-operator-valued measures (POVMs). In the Hamiltonian formulation of quantum mechanics, canonical coordinates are related to PVM. In this paper the results of an analysis of various aspects of applications of POVMs in the Hamiltonian formulation are reported. Several properties of state parameters and quantum observables given by POVMs or represented in an overcomplete basis, including the general Hamiltonian treatment of the Neumark extension, are presented. An analysis of the phase operator, given by the corresponding POVMs, in the Hilbert space and the Hamiltonian frameworks is also given.

  • Received 16 January 2015

DOI:https://doi.org/10.1103/PhysRevA.91.062114

©2015 American Physical Society

Authors & Affiliations

D. Arsenović, N. Burić*, D. B. Popović, M. Radonjić, and S. Prvanović

  • Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

  • *buric@ipb.ac.rs

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Issue

Vol. 91, Iss. 6 — June 2015

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