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arXiv:2306.08928 · IEEE Wireless Communications

Quantum Game Theory Meets Quantum Networks

Indrakshi Dey, Nicola Marchetti, Marcello Caleffi, Angela Sara Cacciapuoti

Published Aug 1, 2024• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/mwc.001.2300288

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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.
Abstract Because of the sustained growth of information and mobile users transmitting a great amount of data packets, modern network performances are being seriously affected by congestion problems. In fact, congestion management is a challenging task that can be roughly summarized as a trade off between transmission latency and cost. In this context, a novel framework is proposed for solving the congestion problem on communication networks using a quantum game theory model, where network packets compete selfishly for the shortest route. Simulations show that final network routing and traveling times achieved with the quantum game version outperform those obtained classically. This leads to the opportunity of developing full-stack protocols that may be capable of taking advantage of the quantum properties for optimizing communication systems. Due to its generality, the game theoretic approach can be applied both in local networks and in more complex networks such as 5G or LTE-A.
Because of the sustained growth of information and mobile users transmitting a great amount of data packets, modern network performances are being seriously affected by congestion problems. In fact, congestion management is a challenging task that can be roughly summarized as a trade off between transmission latency and cost. In order to contribute to solve the congestion problem on communication networks, a novel framework based on a quantum game model is proposed, where network packets compete selfishly for their fastest route. Simulations show that final network routing and traveling times achieved with the quantum version outperform those obtained with a classical game model with the same options for packet transmission for both. Pareto optimality and Nash equilibrium are studied as well as the influence of simulated and real noise in the quantum protocol. This leads to the opportunity of developing full-stack protocols that may be capable of taking advantage of the quantum properties for optimizing communication systems. Due to its generality, this game approach can be applied both in classical complex networks and in future quantum networks in order to maximize the performance of the quantum internet.
In order to analyze the power control problem, the wireless quantum network nodes are modeled as players at a quantum game. The power control problem is one of the most significant wireless communications challenges which characteristics make it proper to be modeled by means of game theory techniques. The problem results in non-cooperative game by nature, but, under quantum rules, a larger strategy space leads the players to choose a coalition strategy as the best option. Thus, the use of quantum game strategies makes possible the emergence of new equilibrium, which guarantees the best possible performance to the whole network. We show also that the whole network power consumption decreases when the intrinsic parallel behavior of quantum computation is capitalized. Moreover, the design of efficient medium access control algorithms is possible.
Coordination is a fundamental primitive in communication and information theory, in which distributed systems must collectively generate correlated behavior rather than merely exchange messages. In quantum networks, the nature of entanglement, quantum measurements, and nonclassical correlations introduces coordination possibilities unavailable classically. This article reviews recent advances in coordination over classical and quantum communication networks, focusing on empirical and strong coordination in multi-user settings. We consider the implications of coordination for nonlocal games, showing how it provides a natural framework for understanding the correlations that enable spatially separated players to improve their probability of winning. We present a unified framework for coordination using classical or quantum communication and pre-shared correlation resources. The review covers simulation of both entanglement and separable correlations across a variety of network architectures, including two-node, cascade, broadcast, and multiple-access networks. We study the operational differences between empirical and strong coordination, and the tradeoffs between communication and correlation resources, such as pre-shared randomness and entanglement. Coordination plays a major role in device-independent quantum key distribution (DI-QKD) schemes, in which parties can generate a secret key even if the devices used in the process have been prepared by an adversary. Furthermore, we examine the role of coordination in quantum repeaters, where distributed entanglement serves as a resource for long-distance quantum communication. The review highlights connections between coordination theory and applications such as distributed quantum systems, quantum internet architectures, and future communication networks.
Topology is one of the most critical properties of networks. Quantum networks, as a new type of network, have fundamentally different principles for establishing connections compared to classical networks, leading to distinct challenges in topology design. Finding the optimal topology for quantum networks to meet traffic demands is a crucial yet not fully understood problem. In this paper, we explore the topology design problem for quantum networks, considering both resource allocation and entanglement distribution. We propose and investigate both flow-based and path-based formulations, along with their associated solutions, aimed at minimizing the topology cost. For the path-based formulation, we also provide the first theoretical analysis of the cost associated with swapping strategies over a quantum path. Extensive simulations demonstrate that our enhanced path-based formulation is both efficient and effective.
Quantum teleportation is a fundamental protocol enabling the transfer of quantum states between remote nodes without physical transmission. As the Quantum Internet evolves, optimizing quantum teleportation becomes crucial due to entanglement degradation, resource constraints, and network efficiency. This paper proposes a game-theoretic framework for managing quantum teleportation by modeling quantum nodes as rational agents competing or cooperating to maximize teleportation fidelity and entanglement utility. We introduce cooperative and non-cooperative game models, analyze Nash equilibrium strategies for teleportation efficiency, and propose a Shapley-value-based entanglement allocation for fair resource distribution. Our system model incorporates graph-theoretic representations of quantum networks, utility functions, and incentive mechanisms to encourage efficient teleportation strategies. A Qiskit-based simulation evaluates teleportation fidelity and resource efficiency, comparing game-theoretic strategies with classical resource allocation methods. Our findings demonstrate that game-theoretic approaches significantly enhance teleportation efficiency, entanglement utilization, and robustness in a dynamic Quantum Internet environment.