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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.

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Authors and Affiliations

  1. Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, 20014, Turku, Finland

    Pekka Lahti & Juha-Pekka Pellonpää

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  1. Pekka Lahti
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  2. Juha-Pekka Pellonpää
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Correspondence to Pekka Lahti.

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Dedicated to Peter Mittelstaedt in honour of his eightieth birthday.

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Lahti, P., Pellonpää, JP. On the Complementarity of the Quadrature Observables. Found Phys 40, 1419–1428 (2010). https://doi.org/10.1007/s10701-009-9373-y

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