On the complementarity of the quadrature observables
arXiv:0912.3384 · doi:10.1007/s10701-009-9373-y
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 tranform 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.
Dedicated to Peter Mittelstaedt in honour of his eightieth birthday
References in corpus (5)
- Quantum Homodyne Tomography as an Informationally Complete Positive Operator Valued Measure
- Position and momentum tomography
- Measuring position and moment together
- A proof for the informational completeness of the rotated quadrature observables
- Quantum tomography, phase space observables, and generalized Markov kernels