Canonical and measured phase distributions

U. Leonhardt, J. A. Vaccaro, B. Böhmer, and H. Paul
Phys. Rev. A 51, 84 – Published 1 January 1995
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Abstract

We derive relationships between canonical and measured phase distributions for quantum-oscillator states in the semiclassical regime. First, we extend the formalism for the canonical phase to include external measurement-induced uncertainty. We require that a phase shifter shifts a phase distribution while a number shifter does not change it. These axioms determine pure canonical phase distributions uniquely while a noisy distribution can be interpreted as a weighted average of pure phase distributions. As a second step, we show that measured phase distributions, i.e., s-parametrized phase distributions fulfill approximately the axioms of noisy canonical phase, and we derive simple analytical expressions for the corresponding weight functions. Our analysis thus bridges all three conceptions of quantum-optical phase (canonical phase, s-parametrized phase, phase from measurements) and provides important physical insight into the relationship between them.

  • Received 27 June 1994

DOI:https://doi.org/10.1103/PhysRevA.51.84

©1995 American Physical Society

Authors & Affiliations

U. Leonhardt, J. A. Vaccaro, B. Böhmer, and H. Paul

  • Arbeitsgruppe ‘‘Nichtklassische Strahlung’’ der Max-Planck-Gesellschaft an der Humboldt-Universität zu Berlin, Rudower Chaussee 5, 12484 Berlin, Germany

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Issue

Vol. 51, Iss. 1 — January 1995

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