Cloning Games, Black Holes and Cryptography
Alexander Poremba, Seyoon Ragavan, Vinod Vaikuntanathan

TL;DR
This paper introduces a new analytical framework for cloning games, providing stronger security bounds and applications in black-hole physics and cryptography, including novel unclonable encryption schemes.
Contribution
It develops a toolkit for analyzing cloning games with new bounds, and applies it to black-hole information scrambling and cryptographic unclonable encryption.
Findings
Binary phase cloning games are $t$-copy secure for $t=o(n/\log n)$.
Achieves optimal bounds of $O(2^{-n})$ for constant $t$.
Provides new unclonable encryption schemes and insights into black-hole information scrambling.
Abstract
In this work, we introduce a new toolkit for analyzing cloning games, a notion that captures stronger and more quantitative versions of the celebrated quantum no-cloning theorem. This framework allows us to analyze a new cloning game based on binary phase states. Our results provide evidence that these games may be able to overcome important limitations of previous candidates based on BB84 states and subspace coset states: in a model where the adversaries are restricted to making a single oracle query, we show that the binary phase variant is -copy secure when . Moreover, for constant , we obtain the first optimal bounds of , asymptotically matching the value attained by a trivial adversarial strategy. We also show a worst-case to average-case reduction which allows us to show the same quantitative results for the new and natural notion of Haar cloning…
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