Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

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.

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.

Paper Structure

This paper contains 24 sections, 2 theorems, 30 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theoretical Foundations
  3. From Classical Correlation to Information-Theoretic States
  4. Non-Separable Dependence in Financial Networks
  5. Scope of the Analogy
  6. Latent Information and Structural Transitions
  7. Summary
  8. The Quantum Network of Assets (QNA)
  9. Market State as a Density Matrix
  10. Entropy and Mutual Information
  11. Purity Index and Entanglement Risk Index (ERI)
  12. Quantum Early-Warning Signal (QEWS)
  13. Interpretation
  14. Data and Implementation
  15. Data
  16. ...and 9 more sections

Key Result

Lemma 3.1

Let $\rho$ be defined by eq:density_matrix_def. Its entries satisfy where off-diagonal terms $(j\neq k)$ encode cross-sectional structural coupling that is not captured by covariance alone. $\blacktriangleleft$$\blacktriangleleft$

Figures (3)

  • Figure 1: QNA processing pipeline: from market data to structural dependence indicators.
  • Figure 2: Standardized benchmark dynamics in the 2020--2025 main sample. The shaded region marks the 2024--2025 visual spotlight used for the non-crisis zoom-in, while the full series retains the pandemic and 2022 tightening regimes. QNA entropy moves closely with classical spectral benchmarks at the regime level, but not one-for-one.
  • Figure 3: Two-stage tariff episode, December 2024 to May 2025. The dashed and dotted lines mark the February 18 initial tariff announcement and the April 2 reciprocal tariff escalation. QEWS (ERI) is compared with rolling-z covariance spectral entropy and rolling-z effective rank.

Theorems & Definitions (11)

  • Definition 1: Rolling Feature Amplitude Vector
  • Definition 2: Market Density Matrix
  • Lemma 3.1: Cross-Asset Structural Coupling
  • proof
  • Proposition 3.2: Separable Limit and the Classical Baseline
  • proof
  • Definition 3: Von Neumann Entropy
  • Definition 4: Mutual Information Between Market Partitions
  • Definition 5: Purity ("Quantum Index")
  • Definition 6: Entanglement Risk Index (ERI)
  • ...and 1 more