Task-Directed Spectral Design for Local Quantum Tomography

arXiv:2610.33723v1 Announce Type: new Abstract: Many tomography tasks require only a low-dimensional function of the state. We study local pure-state tomography under projective-fidelity access when a parametric model, a credible center, and a differentiable downstream task are known before acquisition. The pullback Fubini--Study metric and the task metric define coordinate-invariant generalized eigendirections, which we realize as a fixed library of geodesic fidelity probes.