Abstract Under unitary quantum mechanics, decoherence redistributes information into systemenvironment correlations but does not destroy it. The statement that information remains "in the environment" is operationally incomplete: it may be globally present without being locally readable or actively recoverable under realistic constraints. We distinguish three notions-presence, readability, and recoverability-and show that they are operationally distinct. In controlled simulations of four decoherence models (random circuits, Trotterized Ising, isotropic Heisenberg, CNOT fan-out), we find that recovery is inverse-specific: the correct inverse of the decoherence process succeeds while generic circuits of com parable depth fail. Coupling geometry further shapes accessibility: anisotropic Ising and isotropic Heisenberg dynamics exhibit sharply different local capture structure despite comparable scalar decoherence indicators. On superconducting (Rigetti Ankaa-3) and trapped-ion (IonQ Forte) hardware, exact inverse recovery remains observable on both platforms. On IonQ, the geometry-depen dent capture separation between Ising and Heisenberg dynamics reappears (∼ 10 × in capture efficiency), while on Rigetti it is suppressed to the noise floor by routing overhead—indicating that local accessibility is more hardware-sensitive than global recoverability. The central empirical result is not that exact inversion can restore decohered correla tions—a consequence expected under unitary control—but that decoherence models with comparable scalar indicators and identical global recoverability can produce sharply different local accessibility structures, and that this difference is selectively visible depending on hardware compilation overhead. These results do not establish asymptotic hardness barriers or distinguish between interpretations of quantum mechanics. They support a narrower conclusion: the operational accessibility of decohered information is determined by coupling geometry, not merely by the degree of decoherence, and whether it remains readable or recoverable depends jointly on interaction structure, observer access, and available control operations.
Abstract Under unitary quantum mechanics, decoherence redistributes information into systemenvironment correlations but does not destroy it. The statement that information remains "in the environment" is operationally incomplete: it may be globally present without being locally readable or actively recoverable under realistic constraints. We distinguish three notions-presence, readability, and recoverability-and show that they are operationally distinct. In controlled simulations of four decoherence models (random circuits, Trotterized Ising, isotropic Heisenberg, CNOT fan-out), we find that recovery is inverse-specific: the correct inverse of the decoherence process succeeds while generic circuits of com parable depth fail. Coupling geometry further shapes accessibility: anisotropic Ising and isotropic Heisenberg dynamics exhibit sharply different local capture structure despite comparable scalar decoherence indicators. On superconducting (Rigetti Ankaa-3) and trapped-ion (IonQ Forte) hardware, exact inverse recovery remains observable on both platforms. On IonQ, the geometry-depen dent capture separation between Ising and Heisenberg dynamics reappears (∼ 10 × in capture efficiency), while on Rigetti it is suppressed to the noise floor by routing overhead—indicating that local accessibility is more hardware-sensitive than global recoverability. The central empirical result is not that exact inversion can restore decohered correla tions—a consequence expected under unitary control—but that decoherence models with comparable scalar indicators and identical global recoverability can produce sharply different local accessibility structures, and that this difference is selectively visible depending on hardware compilation overhead. These results do not establish asymptotic hardness barriers or distinguish between interpretations of quantum mechanics. They support a narrower conclusion: the operational accessibility of decohered information is determined by coupling geometry, not merely by the degree of decoherence, and whether it remains readable or recoverable depends jointly on interaction structure, observer access, and available control operations.
This work proposes an operational framework, denoted OFID-G, to investigate whether quantum coherence remains fully reconstructible from locally accessible information, even when global unitary evolution is preserved. The framework is formulated within the Ontological Framework of Imbricated Degrees (OFID), in which physical states may involve degrees of freedom that are not fully accessible within a given local observational regime. Within this perspective, OFID-G defines a possible structural limitation on the local accessibility of coherence, without introducing any modification to quantum dynamics. The central concept is regime-dependent reconstructibility: coherence is said to be reconstructible if a single recovery operation, fixed by calibration alone, can operationally recover it across a tomographically informative family of preparations, and non-reconstructible if a persistent limitation remains despite such procedures. This state-independent formulation anchors the criterion in the theory of approximate recoverability of quantum channels. Rather than predicting a specific mechanism, the framework defines a falsifiable structural criterion distinguishing reconstructible and non-reconstructible regimes, based on controlled variation of physically relevant parameters. The approach remains fully compatible with standard quantum mechanics and does not invoke collapse models or deviations from unitarity. Its empirical content lies in testing whether all observed decoherence effects can be fully accounted for by known environmental mechanisms. This provides a minimal and operational test of the completeness of standard decoherence modeling, shifting the focus from dynamical mechanisms to structural limitations of information accessibility. The framework is developed within the OFID research program (DOI: 10.5281/zenodo.18868538); its concrete experimental realization is developed in a companion operational paper (DOI: 10.5281/zenodo.19351945). Project page :https://alexsasfrance.github.io/OFID-framework/
This paper introduces an operational framework for quantifying reconstructability in open quantum systems under realistic conditions involving noise, measurement, and recovery processes. While decoherence theory explains the suppression of interference due to system–environment interactions, it does not directly address whether quantum states remain reconstructable in practice. To bridge this gap, this work proposes the Recoverability Index (RI), a scalar diagnostic that quantifies how close a system remains to reconstructable dynamics. The RI integrates three key components: recovery fidelity, entropy-like proxies of environmental information dispersal, and distinguishability of environmental records. Unlike traditional approaches that focus on coherence loss, this framework emphasizes reconstructability as an operational criterion, enabling a practical distinction between recoverable and effectively irreversible regimes. A simplified quantum error correction (QEC) scenario is used to demonstrate the applicability of the RI. The results show that the RI provides a transparent and interpretable metric for comparing noise conditions, evaluating recovery performance, and identifying boundaries of reconstructability. This work does not propose a new fundamental theory of quantum measurement. Instead, it offers a tool-oriented extension of the Entropy-Induced Collapse (EIC) framework, focusing on measurable quantities and practical diagnostics. The Recoverability Index serves as a bridge between conceptual descriptions of irreversibility and actionable evaluation in experimental and computational quantum systems. Keywords: quantum decoherence, quantum error correction, recoverability, irreversibility, open quantum systems, quantum information
Quantum information is usually characterized by a state available at a given time and by entropic or channel-theoretic quantities derived from it. We develop a broader operational framework in which entropic content is one coordinate of physical information ratherthan its exhaustive causal description. The primitive structure is an accessibility restriction CX together with an admissible intervention class F. Relative to it we distinguish entropic content S; total and quantum generative capacities GI and GE ; globally produced and regionally accessible causal ecacy gall and gX ; causal shielding fX ; and the local, distributed, recoverable and blocked records of a specied physical history. We retain and unify the mathematically stable results of the preceding programme: S does not determine G in a Rindler family; accessible causal ecacy has an asymmetry-resource structure and can be locked in correlations; horizons can suppress quantum generative structure while preserving entropic or classical content; and local QFT yields complete exterior shielding for genuinely localized, gauge-neutral interventions under the stated assumptions. Rooted causal blocks are introduced as history-labelled points in bres of the restriction map over a local carrier state. The Causal-Fibre Shielding and Recovery Theorem links local equivalence, complete shielding, distributed historical record and future recovery: equal local carrier states imply RX =gX =0, while global distinction implies positive external historical record, quantitatively lower-bounded by binary distinguishability, and any later common map that restores local distinction certies a recoverable fraction of that record. This makes precise the original photon hypothesis: local photon identity need not imply historical-causal identity. We further prove a Bekenstein causal non-exhaustiveness result: for a bounded carrier with xed local Hamiltonian and radius, equal local states have equal entropy, energy expectation and Bekenstein bound, yet may belong to distinct rooted blocks with dierent distributed record and causal futures. This does not violate the Bekenstein entropy bound; it rejects only its interpretation as a complete taxonomy of causal information. The horizon programme is restored through the generative causal residue and causal quality index q, treated as history diagnostics rather than established geometric hair. A structured Causal-Block Completion Hypothesis then introduces a possible universal sector C. In a minimal local scalar realization, Kallen-Lehmann positivity, response-noise consistency, coherent history writing and fth-force constraints turn completion into a positive-measure feasibility problem with a dual no-go certicate. Finally, we dene a microscopic historical causal tension as the extra eld energy required to make a rooted history compatible with present constraints. Its time integral supplies a candidate action scale. A Historical Tension Principle and Historical Backreaction are retained as stronger hypotheses: in a consistent two-boundary completion, the globally realized physical history could depend jointly on past and future boundary data. No alteration of the past is derived by the forward-time theorems. The resulting programme is a falsiable hierarchy from established information identities to a constrained candidate new eld and a separate two-boundary conjecture.
This paper is the seventh in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of objects independently existing within spacetime. Two prior results set up its question. The third paper (Uchida, 2026c) characterized public finality—recoverability of a committed fact by many mutually independent accessors, non-disturbingly and repeatably—as a broadcast redundancy: an effectively classical pointer value proliferated across many disjoint environmental fragments, approximately in the form of spectrum broadcast structure. The fourth paper (Uchida, 2026d) read the evaporating black hole as the regime in which a committed interior record crosses, at the Page time, from hidden to recoverable encoding, reconstructible from the radiation through entanglement-wedge reconstruction; and the parent framework (Uchida, 2026a, §10) had flagged holographic quantum error correction as a place its language of protected, redundantly encoded, locally recoverable records might find content. The present paper makes that content precise as a structure theory of recoverable records, kept separate from any claim of new physics or any suggestion that the framework derives the underlying results. The central claim is conditional and structural. The framework does not claim that every recoverable piece of information is a code, that the universe is literally a quantum error-correcting code, or that AdS/CFT describes our universe. It claims that when information qualifies as an erasure-recoverable record because an encoding preserves a logical degree of freedom—or a logical operator algebra—against a specified family of physical erasures, then that recoverability is formalized as an exact or approximate quantum error-correcting structure, in which each correctable erasure leaves an authorized complementary region supporting a recovery map. That formalization is itself an established mathematical classification; the paper's interpretive contribution is to read the series' recoverable record through it, and to set it against a second, distinct architecture. Broadcast redundancy makes the same effectively classical value legible from many disjoint fragments; erasure-correcting redundancy protects noncommuting logical quantum information by keeping each correctable erased region ignorant of—approximately private with respect to—the protected logical content, while suitable remaining regions recover it. The formal engine of this distinction is the duality between correctability and privacy (the information–disturbance tradeoff), not the no-cloning theorem; no-cloning, with the access structure of quantum secret sharing, survives as the reason independently usable recovery regions for arbitrary unknown logical quantum information must overlap. Three commitments keep the reading honest. First, it separates three senses of "record"—protected logical quantum information, a committed classical record, and a publicly final record—and insists that recovery or decoding restores access to logical quantum information but does not, by itself, commit a classical value; commitment additionally requires measurement, pointer imprinting, decoherence, and stabilization (Uchida, 2026f), and public finality a still later broadcast. Second, holographic quantum error correction is offered as the sharpest worked model of the distinction, with exactly solvable tensor-network toy codes (exact within the model) kept distinct from realistic semiclassical holographic reconstruction beyond those limits (generally treated as approximate), and both from the further question of state-dependence. Third, code-recoverability does not by itself imply public finality: protected quantum information can be recoverable from authorized regions while remaining non-public. The framework relabels code structure as the architecture of recoverability and derives none of it, making no independent empirical prediction. Its disciplined thesis is that codes protect recovery; broadcasts create publicity—different architectures that a single physical history may nonetheless realize in sequence.
When quantum information initially stored in a local qubit disappears, it need not be lost: it may have moved into nearby degrees of freedom or become inaccessible to shallow local control. We introduce finite-window recoverability as an operational channel benchmark that separates these possibilities. It compares optimal recovery from the target site, recovery by a bounded-depth decoder on a finite window, and the unrestricted optimum for that window. Its operational component, local variational recovery, uses local state preparation, window-local control, and target-qubit Pauli readout to certify recoverable memory beyond the target and quantify how much of the same-window advantage is accessible to shallow control. In a disordered kicked-Ising Floquet chain, a depth-6 decoder on a five-site window realizes Q0opt<Q2shallow<Q2opt across the crossover regime, with positive certified gain for most disorder realizations and substantial shallow-accessibility fractions. The signal differs from target-site persistence and reconstructed coherent-information increments. Positive radius-2 gain also persists when the task is embedded in longer open chains using an independent tensor-network backend. Guided by this hierarchy, we test a carrier-deletion task in which the original target register is reset after the dynamics. A depth-8 decoder repairs the input from a radius-3 surrounding halo with held-out median Favg=0.758, above the single-qubit classical benchmark 2/3, and outperforms optimal one-, two-, and three-site halo-subwindow counterfactuals. These results establish finite-window recovery as a local-control benchmark for off-site quantum memory, diagnosing both where local quantum information remains and whether bounded-depth control can refocus it.
This memorandum proposes an operational reinterpretation of wavefunction collapse based on the concept of recoverability in open quantum systems. Rather than treating collapse as a fundamentally distinct and discontinuous physical process, this work suggests that it can be understood as a boundary in recoverability—specifically, the regime in which reconstructability becomes effectively negligible under realistic constraints. From this perspective, the transition from quantum to classical behavior is not associated with a singular event, but with the progressive loss of the ability to reconstruct system–environment correlations. This approach does not deny the empirical phenomena associated with quantum measurement, nor does it propose a new physical theory. Instead, it offers a conceptual framework that connects measurement, decoherence, irreversibility, and information loss through the unifying notion of recoverability. By shifting the focus from observability to operational accessibility, this work provides a complementary viewpoint to standard decoherence-based interpretations. In particular, it emphasizes that irreversibility may arise not from the destruction of information, but from the loss of practical access to it. This memorandum is intended as a conceptual extension of the author’s previous work on operational recoverability metrics and is presented as a philosophical perspective rather than a testable physical model.