The Killing Form and Petz Uniqueness of Gaussian Bures Geometry
For centered bosonic Gaussian states, the covariance pullback of the Bures cometric differs from the lift-normalized classical covariance Fisher--Rao cometric by a state-independent bilinear form. Under the canonical identification of symmetric covariance covectors with $\mathfrak{sp}(2N,\mathbb{R})$, this form is the...