Calibrated Helstrom geometry on the Bloch ball via Connes spectral distance

• URL: http://arxiv.org/abs/2606.13824v1
• Date: Thu, 11 Jun 2026 18:57:14 GMT
• Title: Calibrated Helstrom geometry on the Bloch ball via Connes spectral distance
• Abstract summary: 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.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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