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Helstrom geometry with time-dependent spectral calibration

  • Kaushlendra Kumar
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Abstract

In a recent work we introduced a finite scalar-qubit-scalar spectral triple whose Connes distance reproduces the Bloch-ball trace metric up to a factor 2/Λ, where Λ2=μL2+μR2 for isotropic link strengths μL,μR appearing in the proposed Dirac operator. Here we analyse time-dependent variation of these links, independent of the qubit dynamics. In doing so, we separate the distinguishability and calibration contributions to the spectral rate. A depolarizing example demonstrates spectral growth despite a monotonic contraction of the trace-distance. More generally, we characterize the admissible trace-distance histories compatible with a given positive spectral record and exhibit contracting and reviving realizations. At fixed Λ, we also study a sinusoidal link imbalance that preserves the Dirac spectrum and qubit metric, while the scalar-scalar distance oscillates with half the period of the imbalance.

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Cite

BibTeXRIS
BibTeX
@misc{kumar2026helstrom,
  title = {{Helstrom geometry with time-dependent spectral calibration}},
  author = {Kaushlendra Kumar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33848},
  eprint = {2610.33848},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33848},
}
RIS
TY  - UNPB
TI  - Helstrom geometry with time-dependent spectral calibration
AU  - Kaushlendra Kumar
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33848
UR  - https://arxiv.org/abs/2610.33848
AB  - In a recent work we introduced a finite scalar-qubit-scalar spectral triple whose Connes distance reproduces the Bloch-ball trace metric up to a factor 2/Λ, where Λ^2=μ_L^2+μ_R^2 for isotropic link strengths μ_L,μ_R appearing in the proposed Dirac operator. Here we analyse time-dependent variation of these links, independent of the qubit dynamics. In doing so, we separate the distinguishability and calibration contributions to the spectral rate. A depolarizing example demonstrates spectral growth despite a monotonic contraction of the trace-distance. More generally, we characterize the admissible trace-distance histories compatible with a given positive spectral record and exhibit contracting and reviving realizations. At fixed Λ, we also study a sinusoidal link imbalance that preserves the Dirac spectrum and qubit metric, while the scalar-scalar distance oscillates with half the period of the imbalance.
ER  -