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C. Kerskens

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Preprint Jul 2026

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...

C. Kerskens · 1 citation
Preprint Jul 2026

Gaussian Purification Quotients and Fixed Nielsen Penalties

Information distance and circuit complexity are both obtained by minimizing lengths, but they minimize over different objects. We make this distinction explicit for faithful one-mode Gaussian states. First, invariant-form uniqueness implies that no positive-definite quadratic gate cost can be invariant under the full a...

C. Kerskens · 0 citations
Preprint Jul 2026

The Quantum Correction to Gaussian Information Geometry is the Killing Form of the Symplectic Algebra

On the admissible cone $\mathcal C_\Omega=\{\Sigma\in\mathrm{Sym}^+(2n):\Sigma+i\Omega\ge0\}$ of Gaussian covariance matrices, the classical Bures--Wasserstein transport metric, the Fisher--Rao information metric, and the quantum Bures metric are individually well understood, but their mutual relationship is obscured b...

C. Kerskens · 0 citations

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