Computational Monogamy of Entanglement and Non-Interactive Quantum Key Distribution

2025-10-01

AI Summary

This work resolves the long-standing open problem of non-interactive quantum key distribution (QKD): achieving everlasting security—i.e., security against adversaries with unbounded computational power—using only a single round of synchronous message exchange. Addressing the fundamental limitation that all prior QKD protocols require multiple interactive rounds, we introduce a novel theoretical framework based on computational monogamy of entanglement. We establish, for the first time, that entanglement is a necessary resource for achieving everlasting security in the non-interactive setting. Leveraging this insight, we construct a practical protocol employing EPR pairs, standard and Hadamard basis measurements, and post-quantum non-interactive classical key exchange—requiring neither trusted relays nor pre-shared keys. The protocol is compatible with near-term noisy intermediate-scale quantum (NISQ) hardware and can be naturally extended to a two-round variant satisfying the standard definition of everlasting security, thereby bridging the gap between theory and practice in non-interactive QKD.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Quantum key distribution (QKD) enables Alice and Bob to exchange a secret key over a public, untrusted quantum channel. Compared to classical key exchange, QKD achieves everlasting security: after the protocol execution the key is secure against adversaries that can do unbounded computations. On the flip side, while classical key exchange can be achieved non-interactively (with two simultaneous messages between Alice and Bob), no non-interactive protocol is known that provides everlasting security, even using quantum information. In this work, we make progress on this problem. Our main technical contribution is a computational variant of the celebrated monogamy of entanglement game, where the secret is only computationally hidden from the players, rather than information-theoretically. In these settings, we prove a negligible bound on the maximal winning probability over all strategies. As a direct application, we obtain a non-interactive (simultaneous message) QKD protocol from any post-quantum classical non-interactive key exchange, which satisfies everlastingly secure assuming Alice and Bob agree on the same key. The protocol only uses EPR pairs and standard and Hadamard basis measurements, making it suitable for near-term quantum hardware. We also propose how to convert this protocol into a two-round protocol that satisfies the standard notion of everlasting security. Finally, we prove a no-go theorem which establishes that (in contrast to the case of ordinary multi-round QKD) entanglement is necessary for non-interactive QKD, i.e., the messages sent by Alice and Bob cannot both be unentangled with their respective quantum memories if the protocol is to be everlastingly secure.

Problem

• Developing non-interactive quantum key distribution with computational security
• Establishing computational monogamy of entanglement for cryptographic applications
• Proving entanglement necessity for everlasting security in non-interactive QKD

Innovation

• Computational monogamy of entanglement game
• Non-interactive QKD from post-quantum key exchange
• Protocol uses EPR pairs and basis measurements