Quantum Game Theory meets Quantum Networks

TL;DR

This article introduces a novel game-the-oretical framework for exploiting quantum strategies to solve one of the key functionalities of a quantum network, namely, entanglement distribution and access over any quantum network topology.

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 like entanglement distribution and access, routing, topology extraction and inference for quantum networks. Quantum networks provide the promising opportunity of employing quantum games owing to their inherent capability of generating and sharing quantum states. Besides, 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-theoretical framework for exploiting quantum strategies to solve, as archetypal example, one of the key functionality of a quantum network, namely, the entanglement distribution. We compare the quantum strategies with classical ones by showing the quantum advantages in terms of link fidelity improvement and latency decrease in communication. In 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.

Figures (6)

• Figure 1: Diagrammatic Representation of Quantum Games in Cooperative and Competitive Scenarios. Here 'W' represents winning a particular game-round, while 'L' represents losing that particular game-round. Also it is noteworthy that in a cooperative scenario, though individual players employ individual strategies, action is taken jointly by all the players. While in a competitive scenario, individually different actions are taken by individual players.
• Figure 2: Optimized information and resource flow over a quantum network topology with three leader nodes (Leader), multiple repeaters (R) and end-nodes (E) between A and B; both classical and quantum coalition games are employed and $e_1 \to e_3 \to e_4 \to e_2$ are selected links for information flow.
• Figure 3: Optimized information and resource flow through the control of the next one-hop link within a tree-like quantum network topology; nodes 1 and 6 are the leader nodes that are connected through a fixed link -- Links are selected for information exchange from $A$ to $B$ using a 2-way consensus game. Numbers in red (e.g., $60, 80, 90, \dotso$) are latency-based cost and numbers in teal (e.g., $0.3, 0.4, 0.5, \dotso$) are fidelity-based payoffs. The numbers inside $\{...\}$ represent the identities of the possible next hops, either of which the present node can connect to in the next step.
• Figure 4: Nash equilibrium point between the links for information flow from $A$ to $B$ with the objective of minimizing the number of quantum operations and latency, such that the information is exchanged within the end-to-end coherence time of the link. The cost function for node $A$ and node $B$ is computed using the total latency experienced over all the links that information of the nodes propagates on. These results are based on topology outlined in Fig. \ref{['FIG2']}.
• Figure 5: Variation in the normalized delay experienced by information flow arriving at any end-node within the topology obtained in Fig. \ref{['FIG2']}, as a function of the increasing number of nodes simultaneously communicating over the network. CN stands for Classical Networks and QN stands for Quantum Networks.