(124g) Developing a Quantum Entanglement-Enabled Secret Sharing Strategy for Networked Control Systems

Networked control systems are industrial control systems that utilize data communicated over networked communication channels to operate spatially distributed industrial processes. Anomalies in operational data may pose challenges to the stable and/or profitable operations of the process [1]. Traditionally, the challenges to process stability posed by anomalies in data over networked communication have been addressed via control design (e.g., [2]- [4]) or via network design-based approaches (e.g., [5], [6]). However, certain anomalies (e.g., due to cyberattacks) that result from external malicious incursions into the network cannot be eliminated. Secret sharing strategies that may be utilized to secure the data over a traditional network have been proposed (e.g., [7], [8]). Nevertheless, the proposed approaches may be computationally intensive and may have scalability issues.

In recent years, quantum computers that utilize quantum mechanical phenomena to perform computations (e.g., by applying operators called gates on quantum states) have witnessed rapid development [9]. Quantum computers may be utilized to leverage quantum physics and develop novel approaches for data processing and communication that are not possible using classical physics. An entangled quantum state (e.g., two entangled qubits) may be thought of as an inseparable combination of two qubits, even if they are spatially distant. When one is measured, the state of the other can be known to the individual who measured the first. An entangled pair of quantum states is used in a strategy called the “CHSH game.”

The CHSH strategy describes the sequence of moves two players may make during a game to win against a referee [10]. During the game, the players and the referee exchange numbers that can take values of 0 or 1. The players win the game if the numbers exchanged with the referee satisfy an algebraic equation. During the game, the players cannot communicate with each other; however, they can strategize before the game begins. The CHSH strategy is decided by the players before the game begins and relies on measurements of an entangled quantum state shared between the players. Using the CHSH strategy, the players can win against the referee with a probability of 85%.

This work presents preliminary results on interpreting the CHSH game for two scenarios within the context of a networked control system: 1) from a secret-sharing perspective to enhance network cybersecurity, and 2) from the perspective of stabilizing a process with distributed control system under communication losses including in the presence of a denial-of-service attack. The control of an illustrative spatially distributed process implemented with the aid of a quantum computer is considered. Multiple computing systems (players), which can incorporate quantum computers, are used. In addition to the local quantum computers, a supervisory system is considered as the referee. Classical communication networks are assumed to be present between the referee and the players. Several pathfinding studies are performed under each scenario. Each pathfinding study analyzes the solution to an optimization problem that utilizes a parameterized version of a single qubit gate, and a CHSH-like strategy [11]. Specifically, for the scenario seeking to interpret the CHSH strategy from a secret-sharing perspective, the optimization problem is solved to explore what, if any, approximations of the process state measurements can be exchanged between the referee and the players to ensure system stability, while preserving the confidentiality of the data communicated over the network. For the scenario interpreting the CHSH game from the perspective of stabilizing the process distributed control system under communication losses, the optimization problem is solved to identify if there exist any stabilizing control laws implementable with the aid of quantum information in the presence of partial or full data loss over a network. The results from each scenario are discussed in detail.

References:

[1] X. -M. Zhang et al., "Networked control systems: a survey of trends and techniques," in IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 1, pp. 1-17, 2020.

[2] C. Schlotterbeck, et al., "Stability guarantees for a class of networked control systems subject to stochastic delays." IEEE Transactions on Automatic Control, vol. 69, no. 12, pp. 8884-8891, 2024.

[3] A., Milad, and H. J. Marquez., "Observer-based event-triggered consensus control of multi-agent systems with time-varying communication delays." IEEE Transactions on Automation Science and Engineering, 21.4 (2023): 6336-6346.

[4] Duo, W., et al., “A survey of cyber attacks on cyber physical systems: Recent advances and challenges”, IEEE/CAA Journal of Automatica Sinica, vol. 9, no. 5, pp. 784-800, 2022.

[5] A., Khalifeh, et al., "Wireless sensor networks for smart cities: Network design, implementation and performance evaluation.", Electronics, vol. 10, no. 2, p. 218, 2021.

[6] F., Zhu, et al., "Practical network coding technologies and softwarization in wireless networks." IEEE Internet of Things Journal, vol. 8, no. 7, pp. 5211-5218, 2021.

[7] M. S., Darup, et al., "Encrypted control for networked systems: An illustrative introduction and current challenges.", IEEE Control Systems Magazine, vol. 41, no.3, pp. 58-78, 2021.

[8] A., Suryavanshi, et al., "Encrypted model predictive control design for security to cyberattacks.", AIChE Journal, vol. 69, no.8, p. e18104, 2023.

[9] Q. A., Memon, A. A., Mahmoud, and P., Michael., "Quantum computing: navigating the future of computation, challenges, and technological breakthroughs.", Quantum Reports, vol. 6, no.4, pp. 627-663, 2024.

[10] J. F., Clauser, et al., "Proposed experiment to test local hidden-variable theories.", Physical review letters, vol. 23, no.15, p. 880, 1969.

[11] S. Narasimhan, et al., “Tools to Design Algorithms for Implementing Control Over Quantum

Computers”, In Press, 2025.