Abstract This paper presents a fundamental re-examination of quantum entanglement, nonlocality, and the limits of standard quantum mechanics by introducing a new theoretical framework: No-Signal Control Theory (NSC theory).The approach proposes that a quantum state cannot be fully described within a conventional single-layer Hilbert space. Instead, it must be formulated within a two-layer Hilbert-space structure, consisting of: an observable layer, and a structural layer. This two-layer Hilbert space model provides a unified explanation for several reproducible IBM Quantum device experiments that challenge standard interpretations of quantum mechanics. These experimentally confirmed and highly repeatable effects include: Nonlocal Hadamard switching: the H-gate changes a remote qubit’s measurement probability (from 0→1/2 or 1→1/2), acting as a nonlocal structural switch without transmitting classical information. CNOT order dependence: the measurement distribution shifts significantly depending on whether the control and target qubits are swapped, indicating a structural asymmetry not accounted for by standard quantum theory. NS/EW basis stability asymmetry: distinct stability differences between the north–south (NS) and east–west (EW) basis states, demonstrating the presence of a hidden structural layer. Collectively, these results suggest that remote operations do not transmit information but do transmit structure, preserving compatibility with the no-signaling principle while revealing a deeper mechanism behind nonlocal quantum behavior.This also connects directly to the proposed PQ (Perception Quantum) Unified Model, which interprets quantum tunneling, CNOT asymmetry, and structural recoil within the same two-layer framework. [Supplementary Material] Title: Visual Guide to NSC Theory and the PQ Hypothesis This supplementary document provides a visual and geometric interpretation of the proposed Two-Story Quantum Structure, complementing the theoretical and experimental results presented in the main paper. Key Contents: Visualization of the Two-Layer Structure:Diagrammatic representations of the Observation Layer (“Window”) and the Structure Layer (“Arrow”). Physical Interpretation of Quantum Gates:How the Hadamard (H) gate rotates the observation layer, and how the CNOT gate copies structural directionality, creating asymmetric recoil effects. Mechanism of Recoil & Tunneling:Intuitive diagrams explaining the “structural recoil” in asymmetric CNOT operations and the time-reversal interpretation of quantum tunneling within the PQ unified framework. This guide is intended to help researchers intuitively understand the physical mechanisms underlying NSC theory, PQ theory, and the proposed two-layer Hilbert-space formulation of quantum mechanics.[Update: November 29, 2025] Added Supplementary Material B: Provides Python source code and experimental records verifying the Nonlocal Structural Switching and Resonance via IBM Quantum hardware. This serves as experimental proof of the NSC Theory.
Abstract This paper presents a fundamental re-examination of quantum entanglement, nonlocality, and the limits of standard quantum mechanics by introducing a new theoretical framework: No-Signal Control Theory (NSC theory).The approach proposes that a quantum state cannot be fully described within a conventional single-layer Hilbert space. Instead, it must be formulated within a two-layer Hilbert-space structure, consisting of: an observable layer, and a structural layer. This two-layer Hilbert space model provides a unified explanation for several reproducible IBM Quantum device experiments that challenge standard interpretations of quantum mechanics. These experimentally confirmed and highly repeatable effects include: Nonlocal Hadamard switching: the H-gate changes a remote qubit’s measurement probability (from 0→1/2 or 1→1/2), acting as a nonlocal structural switch without transmitting classical information. CNOT order dependence: the measurement distribution shifts significantly depending on whether the control and target qubits are swapped, indicating a structural asymmetry not accounted for by standard quantum theory. NS/EW basis stability asymmetry: distinct stability differences between the north–south (NS) and east–west (EW) basis states, demonstrating the presence of a hidden structural layer. Collectively, these results suggest that remote operations do not transmit information but do transmit structure, preserving compatibility with the no-signaling principle while revealing a deeper mechanism behind nonlocal quantum behavior.This also connects directly to the proposed PQ (Perception Quantum) Unified Model, which interprets quantum tunneling, CNOT asymmetry, and structural recoil within the same two-layer framework. [Supplementary Material] Title: Visual Guide to NSC Theory and the PQ Hypothesis This supplementary document provides a visual and geometric interpretation of the proposed Two-Story Quantum Structure, complementing the theoretical and experimental results presented in the main paper. Key Contents: Visualization of the Two-Layer Structure:Diagrammatic representations of the Observation Layer (“Window”) and the Structure Layer (“Arrow”). Physical Interpretation of Quantum Gates:How the Hadamard (H) gate rotates the observation layer, and how the CNOT gate copies structural directionality, creating asymmetric recoil effects. Mechanism of Recoil & Tunneling:Intuitive diagrams explaining the “structural recoil” in asymmetric CNOT operations and the time-reversal interpretation of quantum tunneling within the PQ unified framework. This guide is intended to help researchers intuitively understand the physical mechanisms underlying NSC theory, PQ theory, and the proposed two-layer Hilbert-space formulation of quantum mechanics.[Update: November 29, 2025] Added Supplementary Material B: Provides Python source code and experimental records verifying the Nonlocal Structural Switching and Resonance via IBM Quantum hardware. This serves as experimental proof of the NSC Theory.
Abstract This study demonstrates, through quantum circuit implementation based on ΔLink QESDC and experiments on real hardware, that structural resonance in a quantum system can persist even after measurement, treating this fact as a distinct physical behavior rather than retreating into ambiguous paraphrasing or conventional operational interpretations [4][2]. The prevailing understanding that quantum measurement irreversibly collapses the state, rendering the reuse of quantum resources difficult, is not a necessity derived from the formalism of the theory, but merely serves as a conventional idiom circulated to short-circuit explanation [5][6][7][8][21]. This research focuses on the correspondence between the mathematical fact that the Control-NOT (CX) gate is involutory (CX2=I) and the experimental fact that statistical reproducibility appears consistently on real machines. We present this correspondence not by dismissing it as "coincidence," "noise," or "exception," but by reducing it to the physical meaning of the circuit and measurement [6][10][11][27][3]. To this end, we introduce the NSC (Non-Signaling Control) Dual-Layer Structure Axiom as a minimal logical component, resolving the explanatory gap regarding post-measurement behavior by separating the degrees of freedom updated by measurement from those that can be retained thereafter [6][10][11][27][3]. Furthermore, by contrasting configurations with and without anchor qubits, we experimentally show that while quantum recycling may be partially observed in the initial stages, it is highly likely to destabilize and fail over time in the absence of an anchor [2][3]. In contrast, in configurations introducing an anchor, it was confirmed that the structural layer is retained even across measurements, and the reuse of quantum structural resources is established with statistical stability [1][2][3]. This study does not "follow existing theory as a replacement," but complements the points where existing theory has ceased explanation, based on the irrefutable observational facts of circuit reproducibility and real-machine statistics, thereby forcibly visualizing the physical behavior of resonance structures remaining after observation through the demand for implementation and replication [5][6][7][14][17].
The nonlocal correlations of quantum entanglement, famously described by Einstein as “spooky action at a distance”, have stood as one of the most profound and puzzling features of quantum mechanics since the 1935 EPR paper. Decades of increasingly sophisticated experiments, culminating in loophole-free Bell tests, have irrefutably confirmed that these correlations cannot be explained by any local hidden variable theory. Yet, standard quantum mechanics offers no deeper explanation for this nonlocality—it is simply accepted as a fundamental, irreducible feature of reality. The no-signaling theorem further asserts that this nonlocality cannot be harnessed for superluminal communication, as single measurement outcomes are fundamentally random. This paper challenges this conventional wisdom. It asks a question that strikes at the heart of physical reality: Is quantum entanglement truly fundamental, or is it the manifestation of a deeper, hidden structure? If such a structure exists, it must leave observable imprints. The Instantaneous Teleportation Cosmos (ITC) framework, developed throughout these chapters, proposes precisely such a deep structure: entangled particles are not independent entities, but two ports of the same basal storage unit—a non-spatial, absolutely existing reality from which our four-dimensional spacetime emerges. The ITC framework is built upon four core properties, each derived from first principles, experimental evidence, and rigorous logic: P1 (Storage Perfection): Information in the basal structure is perfectly preserved, never decaying or distorting. This property, rooted in the principle of information conservation, ensures that modulations can be accumulated over time. P2 (Instantaneous Connectivity): Basal nodes are connected without distance or delay. This property, directly motivated by the violation of Bell inequalities, explains the nonlocality of entanglement and provides the basis for the possibility of superluminal communication. P3 (Mapping Determinacy): The projection from a basal state to the statistical distribution in emergent spacetime is deterministic and injective (one-to-one). Determinacy ensures experimental reproducibility, while injectivity guarantees the fundamental distinguishability of different physical states—both prerequisites for science itself. P4 (Manifestation Finiteness): The manifestation of basal information in emergent spacetime requires a local time τ and yields random single outcomes. This property acts as the crucial barrier safeguarding causality, preventing the instantaneous connectivity of P2 from being used for single-shot information transmission, and ensuring compatibility with relativity. These four properties work in synergy. P2 guarantees that a local modulation can affect a distant party. P1 ensures that this effect is accumulable over multiple trials. P3 dictates that a change in the basal state must lead to a change in the statistical distribution at the manifestation layer. P4 explains that while single outcomes remain random, this statistical change manifests as a tiny, detectable shift ΔP in the single-party probability. The central, testable prediction of the ITC framework is that this shift is non-zero: ΔP≠0. This directly contradicts the no-signaling theorem of standard quantum mechanics, which asserts ΔP = 0. Deriving this necessity from the four core properties is a central theme of this theory. The structure of the paper mirrors this logical progression. Chapter 1 re‑examines the no‑signaling theorem, arguing that the existence of the basal structure changes the meaning of local operations—the operation modifies the boundary conditions of the shared storage unit, while the reduced density matrix is merely a projection of the basal state. Hence the theorem holds for finite samples but can be transcended in the infinite‑sample limit. Chapter 2 chains the four properties to rigorously derive that modulation inevitably causes a change ΔP≠0 in the receiver’s single‑party probability. Chapter 3 explores how the bipartite correlation information, lost in the partial trace of standard quantum mechanics, can leave an imprint as ΔP in single‑party statistics under the ITC framework. Theoretical predictions demand experimental tests. Chapter 4 designs an immediately realizable decisive experiment based on demonstrated 10-km trapped-ion entanglement capabilities. By accumulating 245,000 total events (122,500 inside the modulation window) over approximately 30 hours and using a 7σ confidence standard, the experiment will detect ΔP and measure the response delay. If ΔP is significantly non-zero and the delay is much smaller than the light travel time, it would provide the first evidence for a deep structure; if no signal is seen, the one-sided 95% confidence upper bound on ΔP will be constrained below 0.17%, providing the most stringent test of the no-signaling theorem to date. Chapter 5 synergizes the P5 property of SET theory with the π-pulse. By altering the content of the information cluster at the sender (Alice), the π-pulse generates the original probability shift ΔP₀, serving as the source of the signal. Meanwhile, P5 resonance at the receiver (Bob) excites the τ-mode, compressing the manifestation time τ. This reduces quantum fluctuation noise, increases the signal‑to‑noise ratio, and thereby enhances the detectability of ΔP—this process that does not change the signal itself but amplifies its distinguishability within the noise. Working in synergy, these two mechanisms bring ΔP to an experimentally detectable level, ensuring that even a weak initial signal can be reliably captured. This paper presents a coherent, self-contained theory that, starting from the first principles and core properties of ITC theory, predicts observable effects and designs a clear experimental path for verification. Whether the outcome confirms the existence of a deep structure or imposes a more rigorous constraint on the no-signaling theorem, the work herein represents a significant step in our relentless pursuit to understand the ultimate nature of reality.
This volume explains why the standard formalism of quantum mechanics is not merely successful, but structurally inevitable. Rather than proposing a new interpretation or modifying existing equations, this work derives quantum mechanics as the only stable descriptive framework compatible with the FSPS (Foundational Structure / Projected Structure) model. Within FSPS, observable physics (PS) arises as a projection from a non-geometric foundational layer (FS), and this projection necessarily introduces non-commutativity, probabilistic structure, and unitary evolution. The volume combines the axiomatic foundation of FSPS–00 v2.2 with a focused derivation showing that classical mechanics is structurally unstable under projection, while the Hilbert-space formalism of quantum mechanics represents the minimal information-preserving description. Measurement, wavefunction collapse, and probabilistic outcomes are treated not as additional physical processes but as re-projection and stabilization events within PS. No changes are made to Schrödinger dynamics, operator algebra, or experimental predictions. This work serves as a unifying explanation for why quantum mechanics has its present form, consolidating earlier FSPS-based analyses into a single, coherent account aligned with modern quantum theory.
The nonlocal correlations of quantum entanglement have been unequivocally confirmed by experiments, yet standard quantum mechanics regards them as a fundamental, irreducible phenomenon. This paper asks: is there a deeper physical structure underlying entanglement? We propose the Instantaneous Teleportation Cosmos (ITC) framework as a theoretical model for such a deep structure, interpreting entangled particles as dual manifestations of the same basal storage unit. This basal structure possesses four core properties: Storage Perfection (P1), Instantaneous Connectivity (P2), Mapping Determinacy (P3), and Manifestation Finiteness (P4). The main obstacle to superluminal communication lies in P4: the randomness of single-shot measurements prevents direct information extraction. However, P4 does not forbid changes in statistical distributions–local modulation at the sender modifies the boundary conditions of the basal storage unit; through P2, this instantly affects the receiver’s basal state; and according to P3, such a change in the basal state necessarily alters the probability distribution at the receiver’s manifestation layer, manifesting as a tiny shift ΔP in the single-party probability. Based on the breakthrough 10‑km ion‑ion entanglement platform, we propose an immediately realizable experimental scheme: using a 7σ confidence standard, we will detect the significance of ΔP via a two‑sample z‑test, and directly measure the response delay with high‑precision timestamps. If ΔP is significantly non‑zero and the delay is much smaller than the light‑travel time, it would provide the first experimental evidence for the deep structure of entanglement; if no signal is observed, we will place stringent upper bounds on ΔP, thereby imposing the strictest test of the no-signaling theorem to date and severely restricting the possible space for a deep structure. The scheme employs the White Rabbit protocol for sub‑nanosecond time synchronization and includes false‑positive elimination measures such as zero‑entanglement control and fiber‑length variation. All necessary techniques are now mature, allowing the experiment to be performed immediately. This experiment constitutes a decisive test for the deep structure of quantum entanglement; regardless of the outcome, it will deepen our understanding of quantum nonlocality and causality.
This is Paper 142 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops a finite mechanical account of quantum entanglement within pq-spacetime. Entanglement is identified with the persistence of a non-factorable family of admissible future histories. Two measurement regions can therefore appear as separate local systems in emergent spacetime while still remaining projections of one joint finite closure problem. Bell inequality violation follows because the joint outcomes are not generated by two independent local completion families. No-signalling is nevertheless preserved because complete changes to a distant measurement boundary do not alter the local marginal outcome weights. The paper establishes the Entanglement Closure Theorem and distinguishes microscopic non-factorability from observable entanglement after coarse-graining into stable measurement records. It also gives an explicit minimal singlet construction using two opposed history fibers carrying the relevant four-phase weights. The resulting finite ledger is antisymmetric, nonseparable, and exactly balanced at each local wing. Complete changes of basis on the distant side preserve those local marginals. Using the previously derived Hilbert-space and beta-Dirac bridges of pq-spacetime, the paper recovers the familiar spinor overlap law, the quantum singlet correlation, the maximal Bell-CHSH value, monogamy of maximal entanglement, and decoherence through environmental boundary enlargement. The analysis also explains why no preferred measurement ordering is required and why entanglement remains compatible with relativistic causality. The resulting picture is direct. Entangled systems do not exchange superluminal messages, carry classical answer sheets, or require a force acting across space. Their local outcomes arise from one shared finite admissibility structure whose joint correlations are nonlocal while its controllable local statistics remain causal. Entanglement is therefore physically real, nonclassical, and nonlocal in correlation, but not a signalling mechanism.
Quantum mechanics is mathematically complete but conceptually burdened by a discrete‑state ontology that the formalism itself does not require. This paper reframes superposition, measurement, and nonlocality as structural features of unresolved and resolved constraint geometry in continuous fields. In this interpretation, a quantum state is not a catalogue of simultaneous possibilities but the orientation of an unresolved constraint region; measurement is the stabilization of that region under new constraints; and entanglement reflects a single unresolved region spanning multiple subsystems. The standard Hilbert‑space formalism remains unchanged—linearity, projection, the Born rule, and tensor structure all arise naturally from the geometry of unresolved continuity. This framework dissolves the paradoxes associated with collapse, wavefunction ontology, and nonlocal influence, yielding a unified, minimal, and physically intuitive account of quantum behavior that preserves the full empirical power of quantum mechanics while eliminating its metaphysical burdens.