Complete Detector Records and Contextual Source Laws in a Retrocausal Spin Model

Abstract:Detector outcome probabilities can be independent of a later measurement setting even when earlier timestamps, detector seeds, or environmental records depend on that setting. We characterize complete-record preservation for a positive wrapped-Cauchy retrocausal spin source. An antipodal identity yields necessary and sufficient conditions for passive and environmental readouts, and source compensation permits a common normalized analyzer for source spins and prepared continuations. Gaussian controller and reset calculations distinguish inverse raw history weights from normalized thermal operations. A quantum instrument provides an operational benchmark, whereas a setting-dependent separable source produces setting-dependent statistics at an earlier joint probe. For two equal-width contexts, a calibrated weak probe requires a minimum source change of $\operatorname{sech}(2g)/8$ in trace distance for exact protection at every nonzero strength. The signal--source-change tradeoff is sharp for this pair of contexts. A contextual positive-history construction recovers the isolated hidden law and preserves records for a specified class of finite adaptive quantum apparatuses, subject to quantum calibration and restricted field access. Direct readout of an added likelihood field distinguishes two future axes with unit probability. The analytical results are supported by continuous-angle and quantum-trajectory simulations, deterministic quadrature, and exhaustive enumeration of a finite policy class. The analysis concerns the specified statistical models; their microscopic physical realization remains an open question.

arXiv:2609.23255 [quant-ph]

(or arXiv:2609.23255v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.23255 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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