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npj Quantum Information

Entanglement as a fairness mechanism in randomized quantum games

Ri‐Hua Zheng, Yang Xiao, Ye‐Hong Chen, Zhi‐Cheng Shi, Yan Xia

Published Jun 16, 2026• 0 citations
Publisher

Abstract

We propose a framework for quantizing randomized quantum games in which entanglement is examined as a tunable fairness resource without relying on fine-tuned strategy parameters. As a case study of the Monty Hall problem, we show that initial entanglement between host and player registers neutralizes classical asymmetry at the distribution level, driving win-probability distributions under different strategic conditions to converge. Implemented on IBM’s Eagle processors via four-qubit encodings, our experiments span a continuum of entanglement strengths and employ extensive randomized trials over broad strategy ensembles. Although the mean no-switch probability remains fixed at its classical value, stronger entanglement progressively suppresses distributional signatures of asymmetric play, yielding increasingly uniform outcome statistics across adversarial conditions. Within the pure-state setting studied here, these findings provide evidence for an experimentally accessible route to quantify entanglement-enabled fairness in quantum games and suggest relevance to quantum information settings involving strategic decision-making under asymmetry.

DOI
10.1038/s41534-026-01296-x

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We propose a framework for quantizing randomized quantum games in which entanglement is examined as a tunable fairness resource without relying on fine-tuned strategy parameters. As a case study of the Monty Hall problem, we show that initial entanglement between host and player registers neutralizes classical asymmetry at the distribution level, driving win-probability distributions under different strategic conditions to converge. Implemented on IBM’s Eagle processors via four-qubit encodings, our experiments span a continuum of entanglement strengths and employ extensive randomized trials over broad strategy ensembles. Although the mean no-switch probability remains fixed at its classical value, stronger entanglement progressively suppresses distributional signatures of asymmetric play, yielding increasingly uniform outcome statistics across adversarial conditions. Within the pure-state setting studied here, these findings provide evidence for an experimentally accessible route to quantify entanglement-enabled fairness in quantum games and suggest relevance to quantum information settings involving strategic decision-making under asymmetry.
Game theory studies strategic decision-making among rational agents, and many classical games can be mapped onto interaction models such as the Ising model. Quantum game theory extends this framework by allowing players to exploit quantum superposition and entanglement. In this work, we study quantum games using an operator-based formulation derived from the transverse-field quantum Ising model. We show that the Hamiltonian-driven dynamics naturally generate entangling operator which resolve the dilemma in the game settings. This leads to a clear quantum advantage over classical outcomes. Unlike standard quantization schemes based on fixed entangling gates, the present approach enables tunable entanglement, controlled directly by physical Hamiltonian parameters, providing a hardware-relevant perspective on quantum game design.
The classical Monty Hall problem serves as a standard exercise in conditional probability. In this article, we examine its quantum mechanical extension to demonstrate how classical probability distributions are governed by symmetry and entanglement. By mapping the available choices to a three-level quantum system (qutrits) governed by SU(3) symmetry, the game is transformed into a formalized quantum system [1]. We establish that when the choices of the host and player are entangled, the act of revealing a door functions as a symmetry-breaking measurement that physically modifies the state space, illustrating that information acquisition in quantum systems is an active, geometric process with direct analogues in quantum field symmetries [2].
Abstract A quantum version of the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined by considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. We also discuss the influence of noise on the game outcome when the parties play through a noisy quantum channel. The experimental set-up can be used to quickly verify the counter-intuitive result of the Monty Hall problem, adding pedagogic value to the proposal.
Abstract Quantum computing has emerged as a useful resource for winning random games. Monty Hall problem is one such game where the powers of quantum mechanics can be utilized for winning the prize. Our paper depicts this problem as a two-player game, where the two players, i.e. the host and the participant share an entangled quantum state. The entangled state is closely knit with the position of the prize containing door, and the decision of the player i.e. either switch or stay from his initial choice of door. The two players are part of one team as they share a quantum communication channel among them by sharing the entangled state as a quantum resource. This enables them to share share secret information about the position of the price as well as the strategy to opt for winning the game. The article shows a unique way of utilizing three different type of entangled states, 3-qubit symmetric W state, 3-qubit X state, and 5-qubit highly entangled Brown state. Further, the effectiveness of each quantum state as a source of communication in disguise is also compared. All the entangled states under study assure winning the price by the participant. However, each quantum state has different entanglement degree and offer varied merits as per the game setting.
A quantization scheme for the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied from a frequentist perspective by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. A potential application to secure communications of this quantization scheme and its results is also briefly discussed.
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation, and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between quantum computers, it is imperative and crucial to exploit game theory for addressing challenges such as entanglement distribution and access, routing, topology extraction, and inference. Quantum networks provide the promising opportunity of employing quantum games owing to their inherent capability of generating and sharing quantum states. In addition, quantum games offer enhanced payoffs and winning probabilities, new strategies, and equilibria, which are unimaginable in classical games. Employing quantum game theory to solve fundamental challenges in quantum networks opens a new fundamental research direction necessitating inter-disciplinary efforts. In this article, we introduce a novel game-the-oretical framework for exploiting quantum strategies to solve – as an archetypal example – one of the key functionalities of a quantum network, namely, entanglement distribution. We compare quantum strategies with classical ones by showing the quantum advantages in terms of link fidelity improvement and latency decrease in communication. In the future, we will generalize our game framework to optimize entanglement distribution and access over any quantum network topology. We will also explore how quantum games can be leveraged to address other challenges like routing, optimization of quantum operations, and topology design.