Spectrally Selected Causal Self-Memory (SCSM) introduces an interventional criterion for a restricted form of same-sector causal memory in open quantum dynamics. Memory effects are commonly described through non-Markovianity, information backflow, memory kernels, or multitime process tensors. These approaches establish that the past can influence the future, but they do not by themselves isolate the case in which information about an intrinsically selected sector of the system is stored and later acts back on that same sector. In SCSM, the target sector is selected spectrally from the reduced dynamics. The system is encoded into a memory, and two interventions are then compared: one leaves the relevant memory record intact, while the other erases that record without changing the reduced system state at the intervention time. The difference in later trace-norm distinguishability defines an operational causal witness. Positive, zero, and negative values of this witness correspond respectively to protective, neutral, and dissipative self-memory for the selected mode. The paper includes an exactly solvable ternary qutrit model exhibiting open protective and dissipative regions separated by an analytic phase boundary, together with a numerical benchmark on a regular graded SU(2) tower. The deposit also contains the LaTeX source, symbolic and numerical reproduction code, CSV data, figures, and an interactive demonstrator. The qutrit result is reconstructed directly from the channel operators by the supplied Python script. SCSM is not proposed as a criterion for consciousness and is not a replacement for existing descriptions of non-Markovianity. It is intended as a same-sector interventional refinement for isolating reflexive memory effects in open dynamical systems.
Spectrally Selected Causal Self-Memory (SCSM) introduces an interventional criterion for a restricted form of same-sector causal memory in open quantum dynamics. Memory effects are commonly described through non-Markovianity, information backflow, memory kernels, or multitime process tensors. These approaches establish that the past can influence the future, but they do not by themselves isolate the case in which information about an intrinsically selected sector of the system is stored and later acts back on that same sector. In SCSM, the target sector is selected spectrally from the reduced dynamics. The system is encoded into a memory, and two interventions are then compared: one leaves the relevant memory record intact, while the other erases that record without changing the reduced system state at the intervention time. The difference in later trace-norm distinguishability defines an operational causal witness. Positive, zero, and negative values of this witness correspond respectively to protective, neutral, and dissipative self-memory for the selected mode. The paper includes an exactly solvable ternary qutrit model exhibiting open protective and dissipative regions separated by an analytic phase boundary, together with a numerical benchmark on a regular graded SU(2) tower. The deposit also contains the LaTeX source, symbolic and numerical reproduction code, CSV data, figures, and an interactive demonstrator. The qutrit result is reconstructed directly from the channel operators by the supplied Python script. SCSM is not proposed as a criterion for consciousness and is not a replacement for existing descriptions of non-Markovianity. It is intended as a same-sector interventional refinement for isolating reflexive memory effects in open dynamical systems.
Quantum systems are rarely isolated from their surroundings. These hidden environments can retain information and return it later, producing correlated errors in quantum computers and complicating the interpretation of experiments. On a quantum processor, for example, one job can therefore leave an environmental trace that affects the next, even after the qubits themselves have been reset. Learning how this hidden influence persists and affects later behavior is therefore important, but the environment is often impossible to measure directly, and fully reconstructing its effects through tomography rapidly becomes impractical. Here, we introduce a response matrix that uses controlled interventions and observations of the system alone to reveal the temporal structure of environmental memory. The matrix records how future observations change across different controlled histories. Its spectrum characterizes how memory is structured and how it persists under specified system resets, while suitable linear combinations of its entries can rule out specified classical models of that memory. Because its history-future queries can be evaluated independently, numerical response matrices can be assembled in parallel. We establish the framework theoretically, characterize response spectra in an interacting spin process, and certify quantum memory in a two-qubit benchmark. This approach turns system observations into a probe of inaccessible environments and could support the diagnosis of correlated noise, tests of open system models, and memory-aware control design.
Open-systems theory runs together two claims that this paper separates. The first is that Markovianity — the memorylessness of a reduced dynamics — is a property of the system. It is not: a single two-qubit exchange dynamics is non-CP-divisible on the reduced cut and exactly unitary-Markovian on the extended cut, so Markovianity is a property of the tuple (cut, preparation domain, intervention class, time range), fixed only once the cut is named. The second is that (non-)Markovianity decides identity, or that process memory is identity-relevant retained structure. It does not: a Markovian amplitude damping loses the record identity of a class with defect , while a non-Markovian process preserves a shielded identity frame exactly, so the memory coordinate and the identity coordinate are independent, and the correct test is the pair . The paper imports the domain machinery unchanged — CP-divisibility, the operational process-tensor Markov condition, and instrument-specific Markov order — and adds, from the identity architecture, the requirement that identity be judged on the maximal continuation quotient. It closes with the converse question: when is a memory back-path constitutive for identity? A back-path is a constitutive coupling if and only if a causally isolated interruption of it — a severing test — changes admissibility, , or ; and the size of the information backflow is neither necessary nor sufficient for this. What is not delivered is stated throughout: no system cut, no memory time, and no damping rate follows from the law, and the results are the finite-dimensional named-process sector.
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.
We investigate the nature of memory effects in the non-Markovian dynamics of spin-boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its environment. We focus on two such criteria, one based on the dynamical map and the other on single-intervention process tensors, and discuss their connection. We apply these criteria to quench dynamics in spin-boson and two-spin-boson models, computed using a numerically exact method for non-Markovian open-system dynamics based on matrix product operator influence functionals. This method is ideally suited to simulate quantum multitime processes in spin-boson models across broad parameter regimes. We find that, with access to single-intervention process tensors, one can generally predict quantum memory in the dynamics at low temperatures. Given instead only the dynamical map, it is still possible to detect quantum memory in the case of resonant environments at short evolution times. Moreover, we confirm quantum memory in the stationary dynamical regime using process tensors with the correlated steady state of system and environment as initial condition.
This preprint develops a framework for intervention-relative predictive memory: the minimum information that must be retained about the past in order to predict every future experiment allowed by a declared intervention set.For finite-dimensional linear processes, predictive memory is characterized exactly by a reachable-observable quotient and the rank of the corresponding past-future Hankel response matrix. The paper derives finite certification procedures, monotonicity under richer control, a decomposition of memory growth into reachability expansion and visibility activation, symmetry-protected compression, and no-compression results under sufficiently rich intervention algebras.The framework is connected to process-tensor bond rank, hidden-memory realization, and physical memory costs. At a prepare-and-measure temporal cut, linear, classical, and quantum memory are distinguished through ordinary rank, nonnegative rank, and positive-semidefinite rank. A robust quantum-dimension witness is derived for an n-message decoding task.A proposed single-photon spatial-mode experiment provides a concrete test. Phase-coded histories have identical present path-intensity distributions but can be perfectly distinguished by permitted future phase and Fourier operations, giving an ideal response matrix equal to the identity. For 17 modes, sufficiently high decoding success directly certifies a 17-dimensional quantum memory.The paper distinguishes established realization, automata, process-tensor, quantum-control, and factorization results from the proposed synthesis and experimental interpretation. It concludes with two natural next directions: experimental implementation and a multitime completely-positive / PSD-rank theory of intervention-relative quantum memory.
This paper pre-registers the Causal Accumulation Law as a rank-2 causal dynamic fieldtheory, together with its axiomatic foundations, two well-defined limits of the memory kernel(quantum mechanics in the Markovian limit, general relativity in the propagator-dominatedlimit), the informational stress-energy tensor implied by the rank reduction required forcausation, and a causal projection operator on the division algebra tower whose admissiblechain is shown to be unique. The central conceptual claim of the framework is that causationis a physical process rather than a statistical relation: a causal event is a rank-2 bilinearinteraction between two rank-1 prior states whose output projects back to a rank-1 vectorwith necessary information loss. Standard causal inference is recovered as the flat-fieldlimit in which the memory vector is trivial. The phase angle α of the source current isidentified with the order of the fractional covariant derivative, so the four integer corners ofα correspond to specific derivative orders and therefore to specific classical theories: identityat α = 0, Schroedinger evolution at α = 1, classical mechanics with the principle of leastaction at α = 2. The dynamics are unitary at the α = 1 corner,non-unitary in the propagator-dominated GR limit, and quasi-unitary (sectorally preserving)elsewhere. The pre-registration is relative to the Standard Model and ΛCDM test conductedin the companion paper; the present paper establishes what is being evaluated. #Preregistration #FoundationalPhysics #UnitTest. #non-markoviancausality