An earlier note derived, for two qubits coupled by a fixed controlled-NOT and an experimenterwith local capabilities on the target qubit only, that the accessible effects are exactly those of thealgebra A1 = M2 ⊗ span{I, Z}: a non-classical algebra is accessible while the control qubit’s phaseis not. That boundary was derived for a remainder with no dynamics of its own. This note askswhether it is maintained when the remainder evolves freely under a time-independent HamiltonianH = h1 X + h2 Y + h3 Z that is fixed and known, and the experimenter may insert waits ofany chosen duration, adaptively, anywhere in a protocol. The answer is an exact dichotomy. Theaccessible effect set, and its span, remain unchanged under every finite adaptive protocol if andonly if [H, Z] = 0, i.e. h1 = h2 = 0: the remainder may precess about the axis the interaction reads.For every other member of the family the failure is demonstrated operationally — an explicit pairof states that no protocol without waits can distinguish, and the existing readout protocol with asingle wait of duration π/(4|h|) whose acceptance probabilities differ by 1 − n3^4 > 0, n = h/|h|.For the control H = X the accessible span becomes all of M4, by thirteen named protocols; whetherevery effect of M4 is then implementable is left open. Invariance of a protocol’s statistics underchanges of its wait durations is defined and reported separately from preservation of the accessibleset; in this family the two coincide, for a reason that is stated. The closed form of the wait, thecommutation criterion and the span bound are standard material; the contribution is the worked,exactly-verified criterion at both the effect and the span level. Nothing about robustness or genericHamiltonians is claimed. Technical note, not peer-reviewed. The deposit contains the note and areproducibility archive (one exact-arithmetic script with 34 checks, a failure-path harness, the runrecord and a checksum manifest).
An earlier note derived, for two qubits coupled by a fixed controlled-NOT and an experimenterwith local capabilities on the target qubit only, that the accessible effects are exactly those of thealgebra A1 = M2 ⊗ span{I, Z}: a non-classical algebra is accessible while the control qubit’s phaseis not. That boundary was derived for a remainder with no dynamics of its own. This note askswhether it is maintained when the remainder evolves freely under a time-independent HamiltonianH = h1 X + h2 Y + h3 Z that is fixed and known, and the experimenter may insert waits ofany chosen duration, adaptively, anywhere in a protocol. The answer is an exact dichotomy. Theaccessible effect set, and its span, remain unchanged under every finite adaptive protocol if andonly if [H, Z] = 0, i.e. h1 = h2 = 0: the remainder may precess about the axis the interaction reads.For every other member of the family the failure is demonstrated operationally — an explicit pairof states that no protocol without waits can distinguish, and the existing readout protocol with asingle wait of duration π/(4|h|) whose acceptance probabilities differ by 1 − n3^4 > 0, n = h/|h|.For the control H = X the accessible span becomes all of M4, by thirteen named protocols; whetherevery effect of M4 is then implementable is left open. Invariance of a protocol’s statistics underchanges of its wait durations is defined and reported separately from preservation of the accessibleset; in this family the two coincide, for a reason that is stated. The closed form of the wait, thecommutation criterion and the span bound are standard material; the contribution is the worked,exactly-verified criterion at both the effect and the span level. Nothing about robustness or genericHamiltonians is claimed. Technical note, not peer-reviewed. The deposit contains the note and areproducibility archive (one exact-arithmetic script with 34 checks, a failure-path harness, the runrecord and a checksum manifest).
Fix two qubits and one interaction, the controlled-NOT with control 𝑄2 and target 𝑄1. Give an experimenter local capabilities on one qubit only — resets, local unitaries, projective measurements with adaptive classical processing — and no operation on the other qubit except through the fixed gate. What can be detected about the two-qubit input? The accessible effects are derived from the declared operations and compared only afterwards with an algebra. Three results. (1) With capabilities on the target qubit, the span of accessible effects is exactly 𝒜1 = 𝑀2 ⊗ span{𝐼, 𝑍}, and every effect of 𝒜1 is the effect of one finite adaptive protocol: a non-classical algebra is accessible while the second qubit’s phase is not. (2) Restricting the local unitaries to {𝐼, 𝐻} leaves the span unchanged but strictly shrinks the set of implementable effects: two resource sets can distinguish exactly the same input pairs while differing in which exact measurements they can perform. (3) Relocating the capabilities to the control qubit gives span{𝐼, 𝑋} ⊗ 𝑀2; the two sites are exchanged by a symmetry of the gate, their access is incomparable, their common effects are those of an abelian algebra, and four distinctions are accessible from neither. The upper bounds are conserved-quantity arguments of the kind standard in quantum observability and indirect control; the exact effect-level statements are worked examples whose novelty is not claimed. Every identity and example is checked exactly in the accompanying scripts.
A small quantum arrangement — a reader qubit Q₁ coupled to a remainder qubit Q₂ through one fixed gate, with declared operations on Q₁ only — has access to some distinctions of the remainder and not to others. This manuscript follows that arrangement through fourteen research units — thirteen with a model, exact proofs and an executable checker (with certified interval enclosures wherever a propagation is read), and one, the maintenance criterion, a definition with checked decision logic — and organizes what they establish around four distinctions. First, protecting an access restriction is different from preserving the distinctions a reader can use: a universal leakage bound and an exact one-gate value are proved; a reset-based maintenance pulse prolongs limited leakage at the price of previously accessible information, while a reversible pulse prolongs it and preserves the full declared input class. Second, meeting protection criteria does not identify a mechanism: a prepared finite clock-controller meets four declared criteria at four sizes, and so does a static field with the clock decoupled, and so does the clock's free mean field at the largest size. Third, restoring a supporting condition does not necessarily recover the capability: coupling alignment is shown to be a supporting condition of the capability, and a restoring process that improves alignment in six matched realizations meets the full restoration standard in one, misses it narrowly in one and fails in four, while useful access is preserved in none. Fourth, retaining a relation, delivering it to a reader and using it internally are different achievements, and a supplied design's advantage can reverse when its context changes without the comparison identifying the mechanism: a sector record restores access at three of four endpoints under an added permission; an internal coupling improves the primary endpoint without reaching the reference; a two-by-two of axis term and gating cell reverses both contrasts. Each result is stated with what it does not establish. No conclusion about self-maintenance, ownership or experience is drawn. The deposit is a technical manuscript, not peer-reviewed, that consolidates fourteen closed research notes and adds no theorem; the supporting proofs are in the notes. The package contains the manuscript (PDF and Markdown), the fourteen notes with two errata, every checker and its run record, the failure-path harness with its recorded outputs and a release adapter, the two earlier baseline notes, a claim-to-proof map, a correction ledger, a source lock and a manifest with the SHA-256 of every file. Every number printed in the manuscript was read by script from a packaged run record. Running checks/run_all.sh reproduces every checker's recorded summary line with the declared dependencies only (Python 3.11 or later; sympy 1.14, mpmath 1.3, numpy); the harness coverage, including the checkers it does not cover, is stated in §10 and Appendix A. Drafting and computation were AI-assisted under the author's direction. Archive SHA-256: 119d835b2d2e19463f3eb6478ea34ddbdf4deea220a5d6d6fe528dcf7061bedb.
Contrôlabilité indirecte des systèmes quantiques ouverts Dans cette thèse, nous étudions les propriétés de contrôlabilité et d’accessibilité des systèmes quantiques. Nous donnons d’abord une nouvelle démonstration du fait que, de manière générale, les systèmes quantiques ouverts ne sont pas contrôlables. Par contrôlabilité, on entend que, pour toute paire d’états initial et cible du système, il existe un temps fini T>0 et un contrôle u tels qu’en ajoutant u dans l’évolution du système, l’état cible puisse être atteint à partir de l’état initial en un temps T. Nous considérons ensuite un système ouvert bipartite A+B constitué de deux qubits en interaction, A et B, en supposant que seul A est directement affecté par le contrôle u et que seul A interagit avec l’environnement. Nous nous intéressons à la contrôlabilité de B. Nous montrons que les états purs cibles de B ne peuvent pas être atteints en temps fini à partir d’états mixtes initiaux de B lorsque l’état initial de A+B se trouve à l’intérieur de l’ensemble des états. Ensuite, nous étudions s’il est possible de maintenir l’état de B pur pendant un temps positif. Pour trois couplages spécifiques entre A et B, nous trouvons que les seules trajectoires admissibles sont soit constantes, soit non affectées par le contrôle u. Ces résultats apportent une première réponse négative à la question de la manipulation indirecte de B. Enfin, nous étudions l’accessibilité de B, c’est-à-dire la question de savoir si, pour tout état initial de B, l’ensemble des états atteignables contient un sous-ensemble ouvert de l’ensemble des états de B. Pour cette propriété, nous donnons une condition suffisante qui peut également s’appliquer à des cadres plus généraux, tels que ceux rencontrés en théorie du contrôle géométrique.
Preprint and reproducibility archive; not peer reviewed. What this record contains. The full text of the manuscript "Identical Few-Particle Gauge Hamiltonians, Programmable Collective Charge Response" (M. J. Baek), its Supplementary Information with complete proofs, and the archive that certifies every closed-form value the paper states. The result. Few-particle dynamics are routinely used to infer collective response in paired quantum matter. This work constructs finite-range interacting response twins that defeat that inference exactly. For any prescribed finite p, two positive finite-range parents have complete static gauge Hamiltonians that coincide at every Peierls link phase on every sector N ≤ p and first separate at N = p+1; their zero-twist finite-density ground rays are the same Dicke condensate, yet their collective charge curvatures differ extensively. The obstruction has no universal depth, and the paper locates it exactly: the blind depth equals the spectator body order, the algebraic bound is independent of geometric range, and bounded range still bounds depth only through the number of sites a ball can hold — so no arbitrary-depth family of uniformly fixed range is claimed. Conversely, a structurally closed exact-pair tower closes at depth two. What is hidden is designable: with d(d+1)/2 displacement families the whole symmetric response-tensor difference is locally realizable at interior filling, and a triangular-lattice twin pair differs only in shear while both diagonal responses stay equal. A 4×4 hard-core-qubit discriminator gives an exact factor-of-two contrast with an internal null control and a state-preparation certificate in 17 equal-time settings. What is certified, and what is not. Results proved in closed form are stated as theorems and proved in full in the Supplementary Information; results established by exact rational or symbolic computation are labelled computer-assisted and carry the script that produces them; the 16-qubit discriminator is a blueprint with an end-to-end noise simulation, not a hardware demonstration, which is not claimed anywhere. Scope limits, open proof lines and one refuted conjecture are recorded explicitly rather than omitted. The archive. response_twins_unified_v1.0.zip contains the manuscript and Supplementary sources, the proof notes, the complete fail-closed verification harness (31 executed stages in release mode — 27 claim-bearing certificate stages, 1 non-claim diagnostic stage and three fail-closed gates — and 24 in quick mode) with one frozen log per stage, independent reimplementations of the load-bearing calculations, negative controls that must fail, the exact-arithmetic certificates behind every closed-form value in the paper, the figure-generation scripts, the scientific claim and provenance record (79 rows with status and scope notes, 50 of them naming the in-archive script or certificate that checks them, the rest saying in words why not), and a per-file SHA-256 manifest of all 209 payload files. Verifying it. Extract the archive and run python3 REPRODUCIBILITY/run_all.py --mode quick for the fast subset or --mode release for all 31 stages; bash BUILD.sh rebuilds both PDFs from source. The three gates check journal-format limits, the release payload against its manifest, and every number the documentation states about the artefacts. Running the harness does not modify the archive: all runtime output is written outside the immutable tree, so verification cannot invalidate the manifest. README.md separates reproducing the content (TeX Live 2023 or newer) from reproducing the archived PDF bytes, which needs the exact producing build recorded inside the PDFs. Licences. Manuscript, Supplementary Information and documentation CC BY 4.0; source code MIT; certificate data CC0 1.0. LICENSE.md is the authoritative per-file mapping and is included both in the archive and as a separate file on this record.
Habituellement, les systèmes quantiques ouverts sont considérés comme étant sous l'influence du bruit et donc défectueux. D'autre part, un système contrôlé est considéré comme quelque chose de stable et de prévisible. On néglige souvent le fait que ces deux aspects sont très étroitement liés. Un système quantique parfaitement isolé ne sera pas soumis aux influences de l'environnement, mais il est également impossible d'interagir avec lui de quelque manière que ce soit. Contrôler et mesurer un tel système est impossible et n'a donc aucun intérêt technique.Tout système utilisé dans un dispositif technologique doit donc être en contact avec son environnement. La question, qui est le point de départ de cette thèse, est de savoir s'il est possible non seulement de contrôler un système malgré son contact avec un environnement, mais aussi s'il existe des cas où cette interaction peut être nécessaire, ou du moins utile pour certaines tâches de contrôle.La première partie de la thèse se concentre sur une telle tâche, à savoir la purification d'un qubit. Ici, l'environnement est essentiel, afin de servir de puits d'entropie. La simplicité du modèle choisi nous a permis de dériver analytiquement le temps nécessaire au processus de purification pour des contrôles et des interactions arbitraires. Ceci est utile pour les architectures, où des implémentations de diverses configurations sont possibles.La seconde moitié de la thèse couvre un travail plus méthodique. Dans l'exemple de la réinitialisation des qubits, nous voyons que le temps nécessaire pour effectuer la tâche est déterminé par le couplage entre le système et l'environnement. Afin d'exécuter de telles tâches rapidement, nous devons développer un cadre permettant d'analyser les systèmes au-delà de la limite habituelle du couplage faible. Il n'existe à ce jour aucune méthode générale pour la propagation de tels systèmes, qui permette également la thermalisation. La méthode du Hamiltonien de substitution est un candidat prometteur pour capturer la dynamique au-delà de la limite de couplage faible et son extension, le Hamiltonien de substitution stochastique, permet la thermalisation. Nous étendons le hamiltonien stochastique de substitution en introduisant une nouvelle méthode pour effectuer des échanges stochastiques. Cette méthode est ensuite testée sur un modèle d'exemple simple.
This paper gives a precise mathematical form to intrinsic quantum event closure at the qubit level. It distinguishes a complete event, which carries one definite material record, from an ensemble description in which the individual complete-event coordinate is unspecified. The paper first proves that a small set of standard operational requirements uniquely fixes the two-outcome qubit probability law, independently of any particular geometric representation. It then constructs an explicit deterministic realization that applies to both pure and mixed states and reproduces the standard quantum probabilities exactly. A central result is that substantially different geometric partitions of the event space can generate the same complete set of observable probabilities. The paper therefore identifies the invariant physical content not with any single diagram, boundary, or geometric partition, but with the preserved mapping from complete events to material records and the measure carried into those records. A general representation-invariance result formalizes this conclusion. The paper also separates Hamiltonian state evolution from material event closure, assigning them distinct mathematical and ontological roles. The work does not claim a universal solution to quantum measurement, a derivation of the event space from a deeper theory, or an extension to entangled and higher-dimensional systems. It establishes an exact qubit-level framework in which individual events close deterministically while ensemble statistics reproduce the Born rule. The restricted deposit includes the manuscript and a reproducible validation suite containing analytic, symbolic, and numerical checks of the principal results. Optional restricted-access note Restricted research manuscript and accompanying validation suite. Deposited for timestamping, preservation, and controlled scholarly review. Licensed under CC BY-NC-ND 4.0. For Further Information about the ENSO Framework, please contact, Eric Needham: ensotheory1@gmail.com