1204.2956 (Maurice A. de Gosson)

The Optimal Gaussian State Associated with Joint Position-Momentum
Measurements    [PDF]

Maurice A. de Gosson

We will show that given experimental data obtained from joint position and momentum measurements one can construct an optimal pure state approximating the observed quantum state. For that purpose we use a tool from multivariate statistical analysis (the MVE method, which relies on the existence of a minimum volume ellipsoid containing the convex set of data). This allows us to determine the shape of the covariance ellipsoid, which is thereafter calibrated using the expression of the uncertainty principle in terms of the notion of symplectic capacity. We finally use the theory of the Wigner transform to produce the approximating Gaussian state.

View original: http://arxiv.org/abs/1204.2956