Multitime memory beyond the quantum regression theorem in sequential measurement statistics

Abstract

We investigate the presence of memory in the sequential measurement statistics of an open quantum system, as witnessed by the departure from the quantum regression theorem (QRT), that is, the possibility to predict multitime probabilities from the one-time reduced dynamical map. For factorized initial states, we identify an exact decomposition of the two-time propagator into a QRT-like contribution, fully determined by the reduced dynamical map, and a memory term encoding system--environment correlations across the intervention; in the weak-coupling regime, the memory term yields an explicit second-order correction expressed in terms of the reduced map and bath correlation functions. Furthermore, we introduce an operational quantifier of QRT violations based on the distance between exact and QRT-predicted joint probabilities. Benchmarking the framework on a spin--boson model and using a pseudomode embedding as nonperturbative reference, we comprehensively analyze the impact of spectral-density parameters, environmental temperature, and measurement protocols on the non-Markovianity of the multitime statistics. Comparison with a one-time quantifier shows that reduced-state non-Markovianity and multitime memory are related but inequivalent: the latter, as probed through sequential statistics, is intrinsically protocol dependent and can become visible at higher temporal order even when two-time statistics remain compatible with QRT predictions.