l1-norm and relative entropy of coherence as holonomy measures.
Connection to coherence resource theory.
VI. Predictive Signatures and Falsifiability
Explicit formulas (oscillatory V()V(\omega), geometric phase loops, anisotropic decay).
Twin-photon and superfluid interferometer protocols.
Criteria for falsification.
VII. Discussion
Ontological implications: resonance vs location.
Relation to collapse, many-worlds, and decoherence.
Technological implications (quantum networks, topological quantum memory).
Open questions and limitations.
VIII. Conclusion
Summary of formalism, predictions, falsifiable claims.
InterTop as a geometrical alternative.
References
Dark-state entanglement (2025).
2D superfluid tunneling (2025).
Standard decoherence, Zurek's einselection, resource theory.
I. Introduction
A. Motivation: foundational puzzles of superposition & entanglement
The conceptual puzzles of quantum mechanics remain at the heart of modern physics. Two of the most striking features---superposition and entanglement---have defied classical intuition for nearly a century. The superposition principle dictates that a quantum system can evolve as a coherent combination of multiple classically exclusive states, a phenomenon vividly demonstrated in the double-slit experiment. Similarly, entanglement binds distant systems into nonseparable wholes, producing correlations that transcend local descriptions.
Despite their formal elegance within Hilbert space, the ontological status of these phenomena remains unsettled. Do superpositions represent physically real coexistence of alternatives, or merely informational constructs about potential outcomes? Is entanglement a fundamental "glue" of reality, or does its persistence depend on specific environmental conditions?
Decoherence theory has provided one of the most influential accounts: interactions with the environment select preferred pointer states, suppressing interference and yielding the appearance of classicality. Yet decoherence, while operationally powerful, raises deeper questions: why does a particular basis emerge? what defines the "resource" that is lost when coherence decays? and can coherence be stabilized or engineered rather than being a fragile inevitability?
The urgency of these questions has been amplified by recent experimental advances that reveal coherence and entanglement not as absolute, but as tunable and engineerable phenomena. In particular, cavity-mediated dark-state entanglement demonstrates that the lifetime of quantum correlations can be extended orders of magnitude by shaping dissipation. Likewise, the controlled tunneling of vortex--antivortex pairs in 2D superfluids models the spontaneous generation of topological excitations, with effective "masses" that vary according to dynamical conditions.
