Foundations of Physics

, Volume 40, Issue 9–10, pp 1419–1428 | Cite as

On the Complementarity of the Quadrature Observables

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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.

Complementarity Quadrature observables Unsharp quadrature observables Phase space observables Radon transform Tomography observable Statistical method of moments 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Turku Centre for Quantum Physics, Department of Physics and AstronomyUniversity of TurkuTurkuFinland

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