Records and Responses: Dressing-blind theorems for monitored quantum instruments

Abstract

The rigorous operator-theoretic core behind the measurement discipline: a class of monitored quantum systems — latched instruments — in which every observable splits exactly into a record class (diagonal in a fixed, dynamically absorbing pointer decomposition) and a response class (all the off-diagonal support). Five short, machine-certified theorems follow. (T1) Record statistics form a single classical probability space — coincidence rates factorize at diagonal Born weights and every retarded correlator built from records vanishes identically. (T2) Pointer-conditional dressing leaves the entire record algebra invariant as an operator identity while renormalising responses by Franck–Condon overlaps: the same interaction cloud leaves the bills fixed and changes only the responses. (T3) The record channel's LSZ pole residue is exactly 1 and cannot be renormalised, whereas a bare response excitation carries residue Z < 1 with the deficit living entirely in the dressing continuum. (T4) Latched accumulation is a functional of the source alone, independent of any washout applied to unlatched components — each event is billed once. (T5) The additive contact term to which fluctuation–dissipation and Kramers–Kronig reconstructions are provably blind is fixed by the Euclidean zero-frequency value, so local subtraction constants belong to the record side of the split. Each theorem ships with a self-checking program, and the paper is explicit about which parts are standard material made exact and which readings are new. Applications: measurement statistics, Quantum-Darwinism redundancy, spectator-charge accumulation, and the normal-ordering constants in dressed couplings — the same counter/kernel split that separates the bare α₀ = 1/137 from its dressed value.

Keywords

How to cite

Elliman, D. (2026). Records and Responses: Dressing-blind theorems for monitored quantum instruments. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21189012

@techreport{elliman2026recordsresponses,
  author      = {Elliman, David},
  title       = {Records and Responses: Dressing-blind theorems for monitored quantum instruments},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21189012},
  url         = {https://neusym.ai/papers/records_responses}
}