Purity frontiers and optimal copy complexity for qutrit stabilizer measurements
Loading original first page…
Abstract
We determine purity-estimation frontiers under stabilizer operations, bounded unconditional outputs and uniform expectation bias. In every fixed qutrit-register dimension, attaining the physical upper output endpoint requires and suffices to use copies of order the inverse square root of the bias tolerance. A five-block moment polarization, smooth clipping and reciprocal-weighted repair give a log-free upper bound. A likelihood-curvature argument supplies the matching lower order for bounded-real outputs. We also determine exact three-copy single-qutrit frontiers and the nonnegative unbiased copy threshold, dimension squared minus one. Pure-null instrument structure explains the role of outcome information.
Read the full paper in the original PDF.
Edition files
- Purity_frontier.pdf194.2 KiB · pdf
SHA-256
34f72a5434b07f0b26655b660678312432800c328a46b5ce67a961d63a397fc5 - Purity_frontier_package.zip232.6 KiB · package
SHA-256
a420e2af662b0e3c28aafb13f30575ea674e8afed7ddfc88c8fe0d62e5d8ea8b
Available editions
Research details
- Subjects
- Mathematics · Probability and Statistics · Quantum Information Theory
- Keywords
- purity estimation, stabilizer operations, qutrits, copy complexity, uniform expectation bias, quantum measurements
- Manuscript date
- 2026-10-29
- Reader reuse
- none
Copyright2026 Scott Schubr.
Scope
Tight fixed-dimension square-root copy order at the exact physical output endpoint; exact three-copy qutrit purity-output frontiers; nonnegative unbiased copy threshold and pure-null instrument structure.
Disclosures
OpenAI's Codex assisted with exploration, proof checking, code, literature comparison and preparation. The author takes responsibility for the mathematics and accompanying files.
Reproduction
The source package contains the complete editable LaTeX manuscript, matching PDF, build instructions and five exact-arithmetic verification programs.