Quantum Encrypted Control of Networked Systems

TL;DR

This paper introduces Quantum Encrypted Control (QEC) for networked control systems, leveraging entangled Bell states and quantum key distribution to generate identical quantum keys shared by sensor and actuator. The control computations are performed on ciphertext with lightweight exponential–logarithm encryption, reducing computational burden and improving robustness to key errors compared with classical encryption. The framework is extended with stochastic quantization to handle bandwidth constraints and to provide differential privacy for quantum keys, revealing a trade-off between privacy level and quantization error. Theoretical results establish stability under quantum key errors, quantify quantization effects, and demonstrate practical viability through simulations that compare QEC to classical schemes. The work highlights a principled integration of quantum technologies into control systems, offering significant gains in security, efficiency, and resilience.

Abstract

Encrypted control has been extensively studied to ensure the confidentiality of system states and control inputs for networked control systems. This paper presents a computationally efficient encrypted control framework for networked systems enabled by quantum communication. A quantum channel between sensors and actuators is used to generate identical secret keys, whose security is further enhanced through quantum key distribution. These keys enable lightweight encryption and decryption while preserving confidentiality and control accuracy. We develop a novel encryption-decryption architecture for state-feedback control of linear systems based on quantum keys, and characterize the impact of quantum state errors on closed-loop stability. In particular, we establish the existence of a critical threshold on intrinsic quantum noise below which stability is guaranteed. In contrast to classical encrypted control schemes, which may collapse under a single key-bit error, the proposed quantum encrypted control exhibits strong robustness to key imperfections. We further adopt quantization techniques to address the scenarios with limited communication bits in practical situations, and implement privacy protection for quantum keys based on a stochastic quantizer. These results demonstrate that integrating quantum technologies into control systems in a nontrivial and principled manner, even at their current level of maturity, can yield substantial performance gains in reducing computational complexity and improving resilience to key errors while ensuring security against multiple eavesdropping sources.

Figures (6)

• Figure 1: A networked control system.
• Figure 2: Diagrams of classical encrypted control systems.
• Figure 3: Illustration of the key sharing between the sensor and actuator through quantum entanglements.
• Figure 4: The Diagram of the quantum encrypted control system.
• Figure 5: Time evolutions of $\|\mathbf{u}(t)-\mathbf{K}\mathbf{x}(t)\|^2$$\mathsf{QEC}$ in \ref{['eq:example_opendloop']}-\ref{['eq:example_closedloop']} encrypted by $\mathsf{QEC}$\ref{['eq:beta']}-\ref{['eq:dec']} under different quantum error levels $p$.

Theorems & Definitions (9)

• Theorem 1
• Lemma 1
• Theorem 2
• Theorem 3
• Definition 1
• Definition 2
• Theorem 4
• Corollary 1
• Lemma 2