A Statistical Interpretation of Quantum Interference From Probability Structure to Quantum Logic and Algorithmic Meaning

Viktoras Rimsha, Laimontas Rimsha

Published Dec 22, 2025• 0 citations

Abstract

We develop a statistical interpretation of quantum interference in which probabilities, rather than wave amplitudes as primitive objects, form the fundamental descriptive level of quantum phenomena. Interference effects are treated as structural relations between alternative probabilistic contributions, governed by a principle of global consistency (priority of the whole over parts). Within this framework, quantum probabilities are non-Kolmogorovian but remain objectively defined. We show that this interpretation naturally leads to the lattice-theoretic structure of quantum propositions introduced by Birkhoff and von Neumann. Quantum logic thus emerges not as an abstract postulate, but as a structural consequence of quantum probability itself. Finally, we illustrate how this viewpoint provides a clear conceptual reading of quantum algorithms. As an appendix, the Grover search algorithm is analyzed as an example where interference-based probability redistribution can be understood without invoking metaphysical superposition, but purely through statistical structure.

DOI: 10.5281/zenodo.18018478

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