https://neckpinch.com/authors/andrew-lesniewski/New arXiv papers by Andrew Lesniewski, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2606.19493/arxiv:2606.19493Wed, 17 Jun 2026 00:00:00 GMTAndrew Lesniewski — The Bures–Helstrom metric is the minimal monotone Riemannian metric on the state space of a qubit. With the quantum Fisher normalization used here, it identifies the Bloch ball with a geodesic hemisphere of the unit round three–sphere. We describe its Ricci flow explicitly. In a general rotationally symmetric gauge the flow is a coupled system for the radial lapse and warping factor; a single scalar equation appears only after a Hamilton–DeTurck gauge choice. In the corresponding moving DeTurck frame the squared warping function Ψ=Φ² satisfies the linear forced heat equation \beginequation* D_tΨ=Ψ_ss-2, \endequation* while the fixed-lapse coordinate form contains the associated transport term. Since the Bures–Helstrom metric is Einstein, the geometric flow itself is the homothetic shrinker \beginequation* g(t)=(1-4t)g_BH, \endequation* with scalar curvature 6/(1-4t) and extinction time T=1/4. Thus the metric remains inside the monotone cone for all t<T and leaves the cone of nondegenerate Riemannian metrics only through the collapsed limit. We also record the volume–normalized flow, for which the Bures–Helstrom metric is a fixed point. Its linearization is the shifted round–sphere Laplacian Δ_(S³)+3, with spectrum \beginequation* σ_\ell=-(\ell-1)(\ell+3), \endequation* and spectral gap 5 after removal of the scaling mode.Ricci flowRicci solitonsScalar curvatureHarmonic maps & DeTurck trickRotational symmetry & warped productsEigenvalues & spectrum