Purity and Covariance Matrix

Basing on the simplest single-mode field source, we investigate the role of the various covariance matrices for reconstructing the field state and describing its quantum statistical properties. In spite of the fact that the intracavity field is a single-mode field, we take into account the natural multimode structure arising in the field, when it leaves the cavity for the free-space propagation. We show how the purity of the field state can be calculated using the different covariance matrices.