Recorded Quantum Histories: Scheduler-Independent Realization and Its Limits

Linked discovery record only. The full manuscript is hosted on OSF under CC BY-NC 4.0. This Figshare listing contains no copy of the manuscript PDF.Primary manuscript preprint: https://doi.org/10.17605/OSF.IO/KGPSW. The OSF manuscript retains its noncommercial licence. Figshare’s CC BY 4.0 selection applies only to this original discovery-listing text and metadata; it does not relicense the linked manuscript or supporting materials.AbstractWhen do prescribed quantum trials realize a proposed law for their recorded results? We distinguish a positive configuration measurement, realization of its statistics by the named trials, and realization of one common full instrument across schedules. For finite experiments with success prerequisites, we give an exact local compatibility criterion for contraction successes completed by their canonical square-root failures. It yields the same terminal instrument, including residual states, under every exhaustive history-dependent classical scheduler. This equality also holds for reference-entangled inputs. The scheduling argument also covers fixed binary instruments with commuting concurrent branch maps. For two canonical trials whose successes commute up to a unit phase, mutual preservation of their success effects characterizes equality of the recorded-result laws. A qutrit pair has this equality but different residual states; we prove that dimension three is minimal within this setting. A commuting nilpotent family has positive configuration effects and a regular unitary dilation, yet its record law has sharp minimum worst-input error nq − 1 + (1−q)^n under at most n calibrated trials, with n ≥ 2 and 0 < q ≤ 1/n. Canonical execution attains the bound. At q = 1/n, it equals (1−1/n)^n, which tends to e^(−1) as n → ∞. Changing a conditional success effect permits exact realization. These results identify distinct requirements on a measurement law and the fixed processes used to implement it.Journal statusThe following article has been submitted to Journal of Mathematical Physics as manuscript JMP26-AR-02895. This is an unreviewed author-submitted preprint, not an accepted manuscript, journal proof or Version of Record. No journal acceptance or peer-review certification is claimed.Supporting reproducibility materialsCode, frozen outputs, computational addendum and supplementary material remain separately available at 10.17605/OSF.IO/68GNF. This supporting-archive DOI is distinct from the manuscript preprint DOI.Kent Nimmo — Independent Researcher, Vancouver, British Columbia, Canada. ORCID: 0009-0003-8503-8891.