Computational Monogamy of Entanglement and Non-Interactive Quantum Key Distribution
Alex B. Grilo, Giulio Malavolta, Michael Walter, Tianwei Zhang
TL;DR
This work investigates non‑interactive quantum key distribution (NI‑QKD) and the prospect of everlasting security. It introduces a computational variant of the monogamy of entanglement (MOE) game and proves a strong bound on adversarial success when the basis choice is only computationally hidden, enabling a NIKE‑based NI‑QKD construction with weak everlasting security. It further shows how to obtain standard everlasting security in two rounds by combining hash‑based verification with quantum‑proof randomness extraction, all using only EPR pairs and simple basis measurements, and it proves that entanglement is necessary for truly non‑interactive everlasting security. The results bridge a gap between classical non‑interactive key exchange and quantum key distribution, highlight fundamental limits, and point to directions for experimental validation and future strengthening of MOE bounds.
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.