A quantum instrument is not determined by its induced positive-operator-valued measure (POVM) and nonselective channel, yet the global control consequences of this residual branch structure remain incompletely characterized. We study the nondegenerate fiber of instruments with both marginals fixed. The subgroup of outcome permutations preserving the effect tuple acts as the deck group of the ordered outcome-frame covering, and closed loops define a conjugacy-class-valued monodromy representation. Nontrivial monodromy obstructs continuous global branch labeling based only on local process continuity. We construct an explicit cyclic family with a uniform m-outcome POVM and a fixed completely dephasing channel, derive robust overlap-based reconstruction and a conservative finite-sample guarantee, and certify entangled conditional Choi states although the nonselective channel is entanglement breaking. For a noisy cyclic family, we prove an exact minimax separation in conditional feedback: recovery rules restricted to the two marginals and the reported local outcome have optimal worst-sector entanglement fidelity 1/m, whereas an outcome-frame-aware controller attains 1-lambda+lambda/m. The exact minimax value of the missing outcome-frame information is therefore (1-lambda)(1-1/m). The results remain entirely within standard finite-dimensional quantum mechanics and are positioned as an instrument-level, permutation-valued specialization of established Kraus-frame/channel holonomy with a distinct global-labeling and feedback limitation.
Physical Sources, Finite Detectors, Persistent Records, and Actual Events This paper develops a unified account of quantum measurement under the Admissibility and Standing Constraint (AASC) framework, connecting constructed physical sources, quantum instruments, material amplification, finite record retention, event probabilities, and the actuality of measurement outcomes. The paper distinguishes three separate objects: a complete quantum instrument containing all outcome operations, including unresolved and failed outcomes; a material record carried by a physical system whose acquisition and retention can be analyzed; an actual history describing which occurrences belong to one original experimental run. A complete instrument and a persistent material record can be constructed without assuming that linear quantum dynamics alone selects one globally definite original-run history. Conversely, the admission of an actual event does not by itself determine its probability law or conditional quantum state. The physical construction contains two complementary measurement targets: a regulated interacting gauge–Higgs–fermion source with its full source Hamiltonian retained during finite receiver pulses; an explicitly parameterized six-mode cosine circuit with source and pump interfaces, losses, distinguishable outputs, a two-polarization intrinsic-spin receiver, and a finite energy-resolving thermal amplifier. The material-registration chain includes source-code loading, driven conversion, output registration, pump-displacement removal, transfer to an intrinsic material spin, finite Gibbs-collision amplification, endpoint reading, and quiet record retention. Electronic display labels, material flags, missed counts, dark displays, blanks, and unreadable outcomes remain distinct and are retained in the joint error ledger. The paper establishes: informative bounded receivers on an interacting quantum source; finite-pulse calibration with the complete source Hamiltonian retained; a complete monitored detector model; finite preparation and amplification bounds; coherent composition of instruments and records; adaptive record composition; local-instrument compatibility; calibrated affine probability uniqueness; sharp coherent calibration limits; sequential probability laws and compatible conditional states; explicit actual-history requirements. A finite Fourier residual certificate bounds the complete monitored detector instrument over its full
35.587 ms interval by
0.063241 in restricted diamond norm. Exact interval arithmetic gives seeded amplifier endpoint fidelity greater than
0.9999235242 after 1,024 finite collisions, together with an explicit conditional survival bound for a subsequent
100 ms quiet hold. The probability analysis shows that positivity, density-operator dependence, affinity under classical mixtures, and calibration fix the trace probability rule for the declared readout. Approximate sector calibration alone permits coherent deviations of order the square root of the calibration error; stronger linear bounds require additional structure. The paper’s central measurement-theoretic conclusion is deliberately separated from its successful detector construction. A complete instrument admits an exclusive-history completion, but linear quantum dynamics alone does not select one such history. Source-specific preparation, reader analysis, and a bounded counting-law completion supply the additional physical input required to select an actual history. The resulting framework substantially develops the material and probabilistic parts of quantum measurement while isolating apparatus errors, actual-history law, and event-selection assumptions as explicit obligations. The work does not claim to solve every interpretation of the measurement problem, derive a universal collapse law, establish unrestricted detector accuracy, or identify a finite calibration certificate with an experimental calibration. Principal contributions A unified source-to-detector account of quantum measurement. Constructed interacting quantum sources with finite receivers. Six-mode cosine-circuit detector realization. Material registration and finite amplification chain. Two-polarization intrinsic-spin receiver. Finite thermal collision and endpoint-reading model. Full-duration restricted diamond-norm detector bound. Interval-certified amplifier fidelity. Conditional quiet-hold survival bound. Retention of blanks, wrong, unreadable, and missed outcomes. Calibrated affine probability uniqueness. Sequential instruments and compatible conditional states. Explicit separation of complete instruments, material records, and actual histories. Source-specific conditions for actual-event selection. Complete physical error and assumption ledger.
Exact identification of a target instrument need not imply a linear stability bound for nearby observations. We study fixed finite-dimensional complete instruments with rank-one target Choi blocks, all outcomes retained, a fixed diagnostic contamination path with strictly positive branch noise, and an all-device bound on Choi mass outside the target rays. Under these hypotheses, linear prescribed-target certification is equivalent to injectivity of the joint observation and completeness map on the physical target-tangent space. An invisible nonzero tangent yields an exactly feasible positive instrument pair with square-root separation; a separate target-ray condition distinguishes sharp square-root behavior from constant-order ambiguity. For two prescribed three-basis readouts on a four-dimensional incidence-record benchmark, we obtain linear and square-root compatible-instrument radii, respectively. We then distinguish arbitrary probability residuals from simultaneous physical preparation and readout errors. Positivity and normalization give a support-amplitude estimate under which both protocols have linear calibration-only sensitivity, although their responses to contamination and unrestricted probability error differ. A fixed-sample application uses additional exactly trusted references to acquire operator-error bounds and obtain a simultaneous full-instrument confidence statement. A separate named-source power calculation reaches the prescribed error threshold with a conservative sufficient allocation of approximately 6.12 × 10^21 trials. The results concern a fixed laboratory-frame target and supplied common-device and sampling assumptions; they establish neither practical efficiency nor device-independent calibration. Written proofs are supported by exact finite certificates and a returned kernel-checked Lean subset; the full argument is not formalized end to end.