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

Paper: arXiv 2511.21515

Authors: Hui Gong, Akash Sedai, Francesca Medda

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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative quantum-inspired density-operator framework (QNA) to evaluate multi-feature financial market dependencies beyond simple covariance. It maintains mathematical rigor while evaluating the model empirically on a multi-year NASDAQ-100 dataset during key macroeconomic stress events.

Research Flowchart

  flowchart TD
    A["Research Goal: Unified Operator Model for Market Dependence & Risk"] --> B["Inputs: NASDAQ-100 Panel 2020-2025 (Returns, Volatility, Liquidity)"]
    B --> C["Construct Multi-Feature Rolling Trajectories & State Vectors"]
    C --> D["Build Density Operators & Overlap Networks"]
    D --> E["Extract Structural Diagnostics: ERI & QEWS"]
    E --> F["Outcomes: Early-Warning Signals (e.g., April 2025 Tariffs) & Joint Entropy/Purity Analysis"]

Cited References (15)

1. Principal component analysis: a review and recent developments (2016) — link
2. Measuring the frequency dynamics of financial connectedness and systemic risk (2015) — link
3. Quantum Computation and Quantum Information (2012) — link
4. Econometric Measures of Connectedness and Systemic Risk in the Finance and Insurance Sectors (2012) — link
5. Principal Components as a Measure of Systemic Risk (2011) — link
6. Correlation, Hierarchies, and Networks in Financial Markets (2008) — link
7. Networks of equities in financial markets (2004) — link
8. Random matrix approach to cross correlations in financial data. (2001) — link

0 of 15 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.