We study the bound states in the continuum for a system of $n$ two-level quantum emitters, coupled with a one-dimensional photon field, when a single excitation is shared among the different components of the system. The emitters are equally spaced at fixed positions. We first consider the approximation of distant emitters and exhibit degenerate eigenspaces of bound states corresponding to resonant discrete values of the energy. We then consider the full form of the eigenvalue equation, in which the effects of the finite spacing and the field dispersion relation become relevant, yielding significant nonperturbative effects that can lift some degeneracies. We explicitly solve the cases $n=3$ and $n=4$ emitters.

The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multitime correlation functions, thus requiring full access to the total “$\mathrm{system}+\mathrm{environment}$” evolution, and providing a stronger requirement than completely positive (CP) divisibility. Here, we analyze CP divisibility and check the validity of quantum regression beyond the Born-Markov approximation (e.g., the weak-coupling limit) for a class of generalized spin-boson models giving rise to a multilevel amplitude-damping evolution; in all cases, it is possible to engineer the system-bath coupling in such a way that quantum regression is exactly satisfied.

We show that non-Markovian open quantum systems can exhibit exact Markovian dynamics up to an arbitrarily long time; the non-Markovianity of such systems is thus perfectly “hidden,” i.e., not experimentally detectable by looking at the reduced dynamics alone. This shows that non-Markovianity is physically undecidable and extremely counterintuitive, since its features can change at any time, without precursors. Some interesting examples are discussed.

We investigate the validity of quantum regression for a family of quantum Hamiltonians on a multipartite system leading to phase-damping reduced dynamics. After finding necessary and sufficient conditions for the CP-divisibility of the corresponding channel, we evaluate a hierarchy of equations equivalent to the validity of quantum regression under arbitrary interventions; in particular, we find necessary conditions for a nontrivial dephasing to be compatible with quantum regression. In this framework, we study a class of dephasing-type generalized spin–boson models, investigating the existence of qubit-environment coupling functions that ensure the exact validity of quantum regression.

The non-Markovian nature of open quantum dynamics lies in the structure of multitime correlations, which are accessible by means of interventions. Here, by examining multitime correlations, we show that it is possible to engineer non-Markovian systems with only long-term memory but seemingly no short-term memory, so that their non-Markovianity is completely nondetectable by any interventions up to an arbitrarily large time. Our results raise the question about the assessability of non-Markovianity: in principle, non-Markovian effects that are perfectly elusive to interventions may emerge at much later times.