The Global Geometry of the Gaussian Bures Manifold: Admissible Domain, Spectral Boundary, and Asymptotic Classicality

arXiv:2609.17563 · quant-ph · Submitted 2026-07-22 · Read on arXiv

quant-ph

Submitted: 2026-07-22

Updated: 2026-07-22

Terminology

• Trace — 18× in this paper · explained in 2 episodes
• Fisher Information — 3× in this paper · explained in 3 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Admissibility — 1× in this paper · explained in 2 episodes
• Anisotropy — 1× in this paper · explained in 3 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• The Quantum Correction to Gaussian Information Geometry is the Killing Form of the Symplectic Algebra
• Phase space formalism for quantum estimation of Gaussian states
• Information geometry of bosonic Gaussian thermal states
• Even Odd Splitting of the Gaussian Quantum Fisher Information: From Symplectic Geometry to Metrology

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