Structured dephasing from a massive scalar memory field: exact treatment, model-selection pitfalls, exclusion limits, and two kinematic signatures

Abstract

Structured dephasing from a massive scalar memory field What this is -> A model of quantum decoherence, and the record of what happenedwhen it was tested against itself. An earlier version of this work proposed that a qubit's loss of coherence isshaped by an auxiliary scalar field acting as an "informational memory", andreported that an oscillatory decay law fitted simulated data far better than thestandard exponential and stretched-exponential laws. This version retracts thatevidence and reports what survives. What went wrong -> The statistical advantage was an artefact. The simulated databegan at a coherence value above 1 — physically impossible — which no admissiblecompeting model could follow. Once the coherence function is correctlynormalised, the proposed law drops from first to fourth place. Worse, datagenerated by an ordinary structured boson bath, containing no memory field of anykind, are fitted equally well by the same law. Goodness of fit cannot tell the twoapart. Fitted oscillation frequencies are biased estimators of the field mass byroughly 50%. What else failed -> Memory measures do not single the field out either. Atmatched decoherence, an ordinary narrow Lorentzian pseudomode is thirteen timesmore non-Markovian than the field. And the system–field mutual information turnsout to be a function of the coherence alone, for *every* dephasing environment —measuring it is measuring the coherence again in different units. The"informational" reading is not supported and has been dropped. Whether it was already dead -> If the field were fundamental and coupled tomatter density, a spectral threshold in the GHz band would require a Compton rangeof centimetres, exactly where torsion-balance experiments are most sensitive. Aqubit's differential charge under such a coupling — the two states contain the sameatoms and differ only by the transition energy — falls short of observability byabout 35 orders of magnitude. As new fundamental physics, the model is excludedoutright. What survives, and it is testable -> Read instead as an effective mode of thedevice's own environment — a phonon branch, a packaging mode, a structureddefect bath — the model needs no new physics and makes two sharp predictions.The noise spectrum acquires a hard threshold with a square-root edge, absent insmooth Lorentzian environments and resolvable by CPMG noise spectroscopy at the 1%level. And for two qubits at separation *r*, the cross-spectrum is the self-spectrummodulated by sinc(*kr*), whose zeros overdetermine the band edge and theseparation, and whose correlation reverses sign with distance — exchanging whichBell state is protected. Ordinary crosstalk is monotonic in separation and cannotreverse. Why it may be worth reading anyway. -> The methodological lesson generalises wellbeyond this model: in non-Markovian decoherence, fit quality is close to worthlessas evidence, because too many physically different environments produce the samecurve. What discriminates is structure — thresholds, zeros, sign changes — notgoodness of fit. The three admissibility constraints derived here (boundedcoherence, quadratic short-time onset, and the plateau implied by a spectral gap)are cheap to apply and reject most published fitting forms. All numerical results are reproducible: code, seeds, figures and a verificationsuite are included. Status: preprint, not peer reviewed. All data are simulated; nothing hereestablishes that the predicted signatures exist in any real device. The paperstates what would have to be observed, and what would have to be excluded, forthem to count.