Sequential measurement of conjugate variables as an alternative quantum state tomography
arXiv:1205.1238 · doi:10.1103/PhysRevLett.110.010404
Abstract
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner quasi-probability. The proper characteristic function obtained by Fourier-transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasi-characteristic function of the two detectors and that, unknown, of the quantum system. This allows state reconstruction through the sequence: data collection, Fourier-transform, algebraic operation, inverse Fourier-transform. The strength of the measurement should be intermediate for the procedure to work.
v2, 5 pages, no figures, substantial improvements in the presentation, thanks to an anonymous referee. v3, close to published version