Reconstructing a Nonlinear Dynamical Framework for Testing Quantum Mechanics

Alex Chenuaud

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/

Miroslav Pardy

Haifeng Qiu

As a supplement to our previous work, this paper reconstructs the electron’s dynamics as a spatiotemporal topological soliton. We derive the Dirac equation and Zitterbewegung effect from the coupling of massless chiral states and demonstrate that quantum measurement—specifically wave function collapse—is a deterministic nonlinear bifurcation in phase space. This framework establishes quantum mechanics as a macroscopic linear emergence of an underlying, deterministic nonlinear dynamical system.

Gilbert Reinisch

Kaiwen Weng, Guohui Hu, Zhaoyuan Meng

The nonlinear Schrödinger equation (NLSE) is a fundamental model that describes diverse complex phenomena in nature. However, simulating the NLSE on a quantum computer is inherently challenging due to the presence of the nonlinear term. We propose a hybrid quantum–classical framework for simulating the NLSE based on the split-step Fourier method. During the linear propagation step, we apply the kinetic evolution operator to generate an intermediate quantum state. The Hadamard test is then used to measure the Fourier components of low-wavenumber modes, from which an approximate nonlinear potential is reconstructed by classical post-processing. The phase transformation corresponding to the reconstructed potential is then implemented as a diagonal phase operation. To validate the proposed method, we numerically simulate the evolution of a Gaussian wave packet, a soliton wave, snake instability, and the wake flow past a cylinder. The simulation results show that the proposed method captures the dominant wave-function profiles, phase structures, and characteristic nonlinear dynamics. This work provides an implementation-level study and an error characterization to assess accuracy-cost trade-offs in hybrid quantum–classical simulations of nonlinear dispersive wave dynamics.

Marek Czachor