Quantum Network of Assets (QNA): A Density-Operator Framework for Market Dependence and Structural Risk Diagnostics

Abstract

Classical correlation and rolling PCA summarize market dependence through covariance spectra, but they do not provide a unified operator representation for entropy, purity-based mixing, and standardized structural deviations built from rolling multi-feature trajectories. We propose the Quantum Network of Assets (QNA), a quantum-inspired but non-physical density-operator framework in which normalized asset-level state vectors induce a time-varying market operator and an associated overlap network. The framework yields two structural diagnostics: the Entanglement Risk Index (ERI) and the Quantum Early-Warning Signal (QEWS). Using a stable NASDAQ-100 panel over 2020-2025, spanning the pandemic aftermath, the 2022 tightening cycle, and the 2025 tariff repricing episode, we show that QNA entropy remains strongly related to covariance spectral entropy and effective rank at the regime level, but that the method becomes empirically distinct once the operator is constructed from multi-feature rolling trajectories rather than returns alone. In the returns-only limit, QNA lies close to classical spectral summaries; with volatility and liquidity channels included, it captures broader dependence reconfiguration and produces the clearest incremental signal during the April 2025 tariff escalation, when QEWS shifts sharply while rolling-z classical spectral benchmarks move only modestly. QNA therefore does not replace covariance-spectrum methods; instead, it provides a unified operator representation in which entropy, purity-based mixing, and event-aligned structural deviations are analyzed jointly across rolling multi-feature market states.