Calibrated Helstrom geometry on the Bloch ball via Connes spectral distance

Kaushlendra Kumar

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arXiv · 2606.13824

Calibrated Helstrom geometry on the Bloch ball via Connes spectral distance

Kaushlendra Kumar

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Abstract

We show that the equal-prior Helstrom trace-distance geometry of qubit states is recovered from Connes spectral distance in a finite scalar-qubit-scalar model. The two scalar reference sectors couple isotropically to the qubit block through identity Dirac links, so that the full Bloch ball, including mixed states, inherits its standard chordal trace-distance geometry from the finite spectral metric. The scalar-sector distances serve a distinct calibration role: they determine the individual link lengths, satisfy a Pythagorean consistency relation, and reconstruct the middle-sector scale.

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Kaushlendra Kumar. 2026-06-11. Calibrated Helstrom geometry on the Bloch ball via Connes spectral distance. https://arxiv.org/abs/2606.13824

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