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Quantum Entanglement Entropy of the Ghost Cell: A 5-Qubit Formalization of Geometric Transition in a 25-Point Voronoi Tessellation

Authors: Keynan, Maayan;

Quantum Entanglement Entropy of the Ghost Cell: A 5-Qubit Formalization of Geometric Transition in a 25-Point Voronoi Tessellation

Abstract

Classical entropy measures applied to geometric transitions are incomplete: the Shannon entropy difference ΔH between two Voronoi configurations quantifies how much uniformity changed, but not how the change was spatially distributed. Twenty-five orzo grains tossed onto an A4 page produced a Voronoi tessellation studied in two configurations – natural (ground truth) and distorted by a single mislocated seed. MATLAB detected the error before the investigator: a counting discrepancy revealed Cell 16 as an anomalous 8-sided polygon induced by its neighbor Cell 9, the ghost cell, whose boundary had absorbed the displacement. A 5-qubit quantum circuit amplitude-encodes both area distributions with an ancilla qubit as a which-configuration flag. The entanglement entropy (Sₑ = 0.3112 bits) exceeds the classical entropy reduction (ΔH = 0.1080 bits) by a factor of 2.88 – the excess 0.2031 bits encodes the spatial redistribution pattern that ΔH discards. A single seed relocation changes 21.1% of the tessellation’s quantum information, 3 to 5 times the naive expectation, quantifying non-local propagation through Voronoi adjacency. Results are verified across NumPy, Qiskit, and pyqpanda (OriginQ Cloud). This is a single-instance demonstration at human-investigator scale; scaling analysis across larger systems is the subject of ongoing work.

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