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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations Quantum Simulation

Calibrated Helstrom geometry on the Bloch ball via Connes spectral distance

arXiv
Authors: Kaushlendra Kumar

Year

2026

Paper ID

69115

Status

Preprint

Abstract Read

~2 min

Abstract Words

81

Citations

N/A

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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  • 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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2606.13824 [2] arXiv https://arxiv.org/abs/2606.13824 [3] Publisher https://arxiv.org/abs/2606.13824

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