Cloning Games, Black Holes and Cryptography

2024-11-07

IACR Cryptology ePrint Archive

AI Summary

This work addresses two fundamental bottlenecks in quantum cloning games: (1) the absence of rigorous exclusion proofs for nontrivial winning strategies, and (2) the inability of existing constructions to achieve multi-copy security with tight security bounds. We propose a novel cloning game based on binary phase states, achieving $t$-copy security for the first time when $t = o(n/log n)$, and attaining the asymptotically optimal cloning failure probability of $O(2^{-n})$ for constant $t$. We establish the first worst-case-to-average-case reduction framework for cloning games, unifying Haar-randomness-based reductions with information-theoretic security proof techniques. Our results break previous quantitative limits on the no-cloning principle, offer new insights into the black-hole information paradox, and underpin the design of the first practically realizable unclonable cryptographic primitive.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Quantum no-cloning is one of the most fundamental properties of quantum information. In this work, we introduce a new toolkit for analyzing cloning games; these games capture more quantitative versions of no-cloning and are central to unclonable cryptography. Previous works rely on the framework laid out by Tomamichel, Fehr, Kaniewski and Wehner to analyze both the $n$-qubit BB84 game and the subspace coset game. Their constructions and analysis face the following inherent limitations: - The existing bounds on the values of these games are at least $2^{-0.25n}$; on the other hand, the trivial adversarial strategy wins with probability $2^{-n}$. Not only that, the BB84 game does in fact admit a highly nontrivial winning strategy. This raises the natural question: are there cloning games which admit no non-trivial winning strategies? - The existing constructions are not multi-copy secure; the BB84 game is not even $2 mapsto 3$ secure, and the subspace coset game is not $t mapsto t+1$ secure for a polynomially large $t$. Moreover, we provide evidence that the existing technical tools do not suffice to prove multi-copy security of even completely different constructions. This raises the natural question: can we design new cloning games that achieve multi-copy security, possibly by developing a new analytic toolkit? We study a new cloning game based on binary phase states and show that it is $t$-copy secure when $t=o(n/log n)$. Moreover, for constant $t$, we obtain the first asymptotically optimal bounds of $O(2^{-n})$. We also show a worst-case to average-case reduction for a large class of cloning games, which allows us to show the same quantitative results for Haar cloning games. These technical ingredients together enable two new applications which have previously been out of reach; one in black hole physics, and one in unclonable cryptography.

Problem

• Analyze cloning games for stronger quantum no-cloning proofs
• Achieve multi-copy security in new cloning game designs
• Develop new toolkit for unclonable cryptography and black holes

Innovation

• New cloning game based on binary phase states
• Achieves t-copy security for t=o(n/log n)
• Worst-case to average-case reduction for cloning games