Entanglement as a Strategic Resource in Adversarial Quantum Games

TL;DR

This work formulates the Quantum Sabotage Game (QSG), a team-based adversarial quantum game that leverages entanglement to enable correlated sabotage actions and deception. It introduces a formal quantum game-theoretic framework with Quantum Nash Equilibrium (QNE) conditions and compares size-matched classical ($\mathbf{2C,3C}$) and quantum ($\mathbf{2Q,3Q}$) teams under ideal, standard-noise, and hardware-noise scenarios. The results show that multipartite W-state entanglement provides a pronounced coordination and sabotage advantage over classical and Bell-state schemes, with robustness to realistic hardware noise. These findings illuminate potential applications in quantum cybersecurity and adversarial AI, and highlight the need for noise-resilient coordination protocols in practical quantum decision-making contexts.

Abstract

Quantum game theory naturally extends classical strategic decision-making by leveraging quantum superposition, entanglement, and measurement-based pay offs. This paper introduces a novel team-based Quantum Sabotage Game (QSG), where two competing teams, one classical and one quantum-enhanced, engage in adversarial strategies. Unlike classical models, quantum teams can capitalize on entanglement-assisted coordination, enabling correlated sabotage actions that provide a decisive edge in unpredictability and strategic deception. We establish a formal quantum game-theoretic model and derive the Quantum Nash Equilib rium (QNE) conditions for multi-agent interactions. Our approach uses computa tional simulations to directly compare classical and quantum strategic efficiency under ideal conditions, standard quantum noise models, and noise profiles calibrated from real IBM Quantum hardware. Our analysis specifically com pares teams of equivalent size: two-player classical (2C) versus Bell-state (2Q) teams, and three-player classical (3C) versus W-state (3Q) teams. Our results indicate that W-state entanglement significantly enhances both defensive coordi nation and sabotage effectiveness, consistently outperforming standard classical strategies and Bell-state coordination schemes. This quantum advantage is shown to be resilient, persisting even when subjected to realistic hardware noise models. These findings have direct implications for quantum-enhanced cybersecu rity, adversarial artificial intelligence, and multi-agent quantum decision-making, thereby paving the way for practical applications of quantum game theory in competitive environments

Figures (10)

• Figure 1: Accumulated sabotage scores over multiple rounds comparing classical and Hybrid Adaptive Heuristic (HAH) quantum teams. The classical teams (2 players, 2C and 3 players, 3C) follow independent, probabilistic sabotage choices and show minimal score change. Quantum teams (Bell (HAH, 2 players, 2Q) and W-state (HAH, 3 players, 3Q)) leverage perfectly coordinated adaptive rules. The cumulative score lines illustrate strategic performance over time, with the W-state team showing a dominant trajectory due to superior coordination.
• Figure 2: Distribution of sabotage effectiveness scores across classical and HAH quantum teams. Bars indicate the frequency of various score outcomes over a sequence of game rounds. The classical (2C and 3C) teams' scores are centered near zero (Mean = 0.04 and 0.08, respectively). In contrast, the HAH benchmark shows a clear advantage for quantum coordination, with the Bell-state (2Q, Mean = 0.86) and W-state (3Q, Mean = 1.96) achieving high, positive average scores.
• Figure 3: Accumulated sabotage scores over 100 rounds using pure Qiskit circuit strategies under ideal (noise-free) conditions. The 3Q W-State (green) and 2Q Bell-State (blue) teams demonstrate a sustained positive score accumulation, clearly outperforming the 3C (solid red) and 2C (dashed red) classical teams, whose scores fluctuate around zero.
• Figure 4: Effectiveness score distribution of pure Qiskit circuit strategies under ideal conditions. This histogram quantifies the advantage seen in Fig. \ref{['fig:realworld_accumulated']}. The 3Q W-State team (Mean = 0.30) achieves a significantly higher average effectiveness than the 3C classical team (Mean = 0.08). The 2Q Bell-State (Mean = 0.08) also shows an advantage over the 2C classical team (Mean = 0.04).
• Figure 5: Accumulated score trajectories over 100 rounds for classical, Bell-state, and W-state teams under noise-free and standard noise conditions. The solid lines represent the ideal, noiseless scenario (baseline performance), while the dashed lines show performance under depolarizing, amplitude-damping, and bit-flip noise. Under all noise models, the quantum teams' advantages are reduced but generally remain positive, staying above the classical team trajectories.