Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising

Explore the monotonicity of scalar curvature in quantum exponential families for transverse-field Ising chains in this 21-minute conference talk from GSI. Investigate the Petz conjecture, which proposes monotonicity of scalar curvature in state spaces with Bogoliubov-Kubo-Mori metric under increased state mixing. Examine the quantum exponential family as a crucial submanifold in quantum statistical mechanics. Analyze the temperature-dependent scalar curvature monotonicity for various chain sizes, discovering breakdowns in finite-size chains while observing potential monotonicity in non-interacting or infinite-size chains. Consider how finite-size effects may influence curvature through majorization-based monotonicity, providing insights into quantum state space geometry and statistical mechanics.