Purity frontiers and the optimal copy exponent for qutrit stabilizer measurements
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Abstract
We determine exact output frontiers for purity estimation with stabilizer operations and uniform expectation bias. For three copies of one qutrit, a four-outcome measurement attains both nonnegative and bounded-real frontiers. For outputs capped at one minus the bias tolerance, both classes have inverse-bias copy power one half in every fixed qutrit-register dimension; square-root lower bounds and upper bounds with one additional logarithmic factor establish this exponent. We also determine the exact nonnegative unbiased copy threshold of dimension squared minus one and classify three-copy single-qutrit pure-null instruments. The proofs combine phase-space positivity, moment identities, inverse-binomial calibration and one-sided likelihood curvature.
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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
Exact purity-output frontiers for three copies of one qutrit; fixed-dimension square-root copy power for nonnegative and bounded real outputs; sharp unbiased copy threshold and pure-null stabilizer 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 editable LaTeX, build instructions and four exact-arithmetic verification programs.