The Unique Pure Gaussian State Determined by the Partial Saturation of the Uncertainty Relations of a Mixed Gaussian State

Maurice A. de Gosson

Let ρ the density matrix of a mixed Gaussian state. Assuming that one of the Robertson--Schrödinger uncertainty inequalities is saturated by ρ, e.g. (Δ^{ρ}X_1)^2(Δ^{ρ}P_1)^2=Δ^{ρ}(…