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

Version 2 (May 2026): Adds OriginQ Wukong hardware execution (device WK_C180, 8192 shots, 2026-05-01) on superconducting quantum processor, accessed via the QPanda3 Runtime API. The original v1 included only simulator-based verification. All v1 claims unchanged; v2 adds a fifth row to the verification table, a Real-Hardware Confirmation discussion section, and updates the 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 (S_E=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 four exact computational backends (NumPy, Qiskit, pyqpanda DensityMatrix, OriginQ Cloud simulator) and confirmed on real superconducting hardware via the OriginQ Wukong 180-qubit processor (device WK_C180, 8192 shots). The hardware run reproduces the predicted equal-weighting of the ghost cell ancilla (P_absent=0.565, P_present=0.435, bias 0.065) within expected NISQ-era noise. This is a single-instance demonstration at human-investigator scale; scaling analysis across larger systems is the subject of ongoing work.