Positive Hybrid Phase-Space Distributions and Fourier Uncertainty in Quantum Mechanics

Viktoras Rimsha, Laimontas Rimsha

Published May 29, 2026• 0 citations

Abstract

We present a highly condensed application of our analytical method, which integrates quantum probabilities within a common structure of contextual projection. By establishing a strictly positive hybrid-statistical distribution and utilizing abstract dual variables, this approach bridges quantum mechanics with the formalisms of uncertainty analysis and signal processing, without giving rise to negative probability paradoxes. We show how fundamental harmonic analysis theorems (Hardy and Beckner) acquire concrete physical interpretations, establishing minimal energy thresholds, information conservation boundaries, and an intrinsic thermodynamic arrow of time. Finally, we map the utility of this framework to quantum computing diagnostics and quantum optics, supported by our previously published applications in phase space quantum kinetics.

DOI: 10.5281/zenodo.20447675

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