Geometry and Quantum Measurement

William K. Wootters

Jonathan A. Gross, Carlton M. Caves

Eduard Prugovečki

Jincheng Zhang

This paper proposes a novel approach to quantum measurement theory based on the framework of information geometry. We argue that quantum measurement, traditionally viewed through the lens of projection postulate and wave function collapse, can be elegantly described as an optimization problem within the information geometry of the Hilbert space. Specifically, we posit that optimal quantum measurements are those which minimize the information-theoretic distance between the measured state and the manifold representing the possible measurement outcomes. This approach provides a geometric interpretation of measurement, allowing us to design and analyze measurement strategies with a deeper understanding of their underlying geometry. We explore key concepts such as the Fisher information metric, the Riemannian structure of the Hilbert space, and the role of the Born rule as a consequence of minimizing the information-theoretic distance. The core claim is that this geometric perspective offers a more profound and potentially more effective way to understand and implement quantum measurement. Furthermore, we outline a methodology for constructing measurement operators based on the curvature of the information geometry, suggesting avenues for designing novel quantum measurement protocols. ---

Rooke Poole

This release presents PooleQ/P Capture v5.6, a channel-resolved local-geometry framework for analyzing measured binary fields, p-bit samples, readout histories, and quantum syndrome-event data. The method preserves the Poole birth, survival, over-support, and strain channels rather than collapsing them into a single cellular-automaton update. The v5.6 amendment reframes PooleQ/P as a local-geometry spectrometer. It defines a decomposed signature vector[\mathcal S_{\rm Poole}(X)=(R_B,R_H,R_\psi),]where (R_B) measures birth-window or boundary geometry, (R_H) measures high-support geometry, and (R_\psi) measures support-strain geometry. The normalized spectrum (\Sigma_{\rm Poole}) identifies which local Poole geometry carries the measured structure. The included benchmark uses exact active-density matching, IID null controls, and same-density shuffled controls. Because shuffling preserves active-cell count while destroying local geometry, the results support the paper-safe claim that PooleQ/P detects structured local correlation beyond active density alone. This work does not claim to reconstruct unknown quantum states, clone qubits, or demonstrate quantum decoder superiority. It is presented as an interpretable measurement-side feature transform and diagnostic layer for structured binary data.

Edoardo Ballico, Bernardi, Alessandra, Iacopo Carusotto +2 more