Quantum Contextual Identity: A New Paradigm in Quantum Measurement via the ∆Q Metric

This work introduces a novel metric, ∆Q, designed to quantitatively capture contextual transformations in quantum systems. While related to Shannon surprisal, ∆Q diverges from it by measuring the ontological shift in observable identity when transitioning between contexts. The expectation value of ∆Q connects naturally to von Neumann entropy, and the metric provides testable predictions in canonical experiments such as the double-slit setup and the CHSH inequality. Furthermore, a pedagogical unit, the Bent (1 Bent ≡ ln2 nats ≈ 1 bit), is proposed to quantify contextual gain. By framing contextual identity as a measurable and dynamic quantity, this study establishes ∆Q as a new foundation for quantum measurement, with potential applications in quantum information, error correction, and contextual computation.