Checking the "0–1 Superposition" Versus "+1/−1" Measurement-Eigenvalue Interpretation

This note examines whether the common phrase “a superposition of 0 and 1” is conceptually misleading in quantum information. It clarifies that ∣0⟩∣0⟩ and ∣1⟩∣1⟩ are basis-state labels rather than numerical scalar values, while Pauli-ZZ measurement outcomes correspond to the signed eigenvalues +1+1 and −1−1. The paper argues that the proposed +1/−1+1/−1 interpretation is valid at the measurement-output layer, but it cannot replace the full Hilbert-space description of quantum superposition, because coherence and relative phase are revealed by measurements in other bases such as Pauli-XX. A small numerical validation compares coherent superposition with an incoherent ZZ-basis mixture to demonstrate the operational role of off-diagonal coherence terms. The accompanying ZIP archive includes the complete LaTeX source and compiled PDF, together with the generated table files, numerical validation JSON output, and the Python validation script used to reproduce the comparison between coherent superposition and an incoherent ZZ-basis mixture.