On the Complementarity of the Quadrature Observables

: Lahti P, Pellonpaa JP

Publisher: SPRINGER

: 2010

: Foundations of Physics

: FOUNDATIONS OF PHYSICS

: FOUND PHYS

: 9-10

: 40

: 9-10

: 1419

: 1428

: 10

: 0015-9018

DOI: https://doi.org/10.1007/s10701-009-9373-y

: https://arxiv.org/abs/0912.3384

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.