A1 Refereed original research article in a scientific journal
On the Complementarity of the Quadrature Observables
Authors: Lahti P, Pellonpaa JP
Publisher: SPRINGER
Publication year: 2010
Journal: Foundations of Physics
Journal name in source: FOUNDATIONS OF PHYSICS
Journal acronym: FOUND PHYS
Number in series: 9-10
Volume: 40
Issue: 9-10
First page : 1419
Last page: 1428
Number of pages: 10
ISSN: 0015-9018
DOI: https://doi.org/10.1007/s10701-009-9373-y(external)
Self-archived copy’s web address: https://arxiv.org/abs/0912.3384(external)
Abstract
In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables.
In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables.