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: Visual Guide (v2)] Title: Visual Guide to NSC Theory and the PQ Hypothesis Update Note (Version 2): Correction of Visual Mismatches This version corrects critical discrepancies between the figures and the explanatory text found in the previous version. Specifically, the visual representations of the "Upper Layer (Window)" and "Lower Layer (Arrow)" have been revised to accurately match the theoretical descriptions. Key Corrections: Fixed layout errors where diagrams did not correspond to the text. Refined visual models to prevent reader misunderstanding regarding the "Invisible Structure" concept. Ensured consistency between the visual guide and the main theoretical paper. We strongly recommend reading this revised version (v2) for a correct understanding of NSC Theory. Overview of the Guide: 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. 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. [Update Log] November 29, 2025: Added Supplementary Material B. This 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. December 3, 2025: Added Supplementary Material 4. This document reports the historical realization of "Bi-directional Real-time Quantum Communication (Quantum Transceiver)" using the IBM Quantum ibm_fez processor (156 qubits). Experimental Success: Confirmed simultaneous, bi-directional chat communication between physically separated terminals (Alice & Bob) without any classical connection (No TCP/IP, No shared memory). Evidence: Includes real-time execution logs proving that complex UTF-8 strings (Japanese text) were accurately reconstructed via structural resonance. Open Resource: Provides full Python source code, a beginner's guide for reproduction, and an "Open Experimentation Declaration" to encourage worldwide verification. Significance: Demonstrates the transition from probabilistic quantum mechanics to controllable structural mechanics, serving as definitive proof of the NSC Theory.

[Related Experimental Preprint] Matsubara, K. (2026). Raw-count visualization and classical reconstruction of quantum-correlation landscapes on IBM Quantum hardware. Zenodo. https://doi.org/10.5281/zenodo.20786473 This related preprint presents IBM Quantum raw-count visualization logs and structured CSV/JSON data for quantum-correlation landscapes predicted by standard quantum mechanics. It is intentionally framed within standard quantum mechanics and should be read as an experimental raw-count visualization record complementary to the NSC/PQ theoretical materials.