The no-cloning principle has played a foundational role in quantum information and cryptography. Following a long-standing tradition of studying quantum mechanical phenomena through the lens of interactive games, Broadbent and Lord (TQC 2020) formalized cloning games in order to quantitatively capture no-cloning in the context of unclonable encryption schemes. The conceptual contribution of this paper is the new, natural, notion of Haar cloning games together with two applications. In the area of black-hole physics, our game reveals that, in an idealized model of a black hole which features Haar random (or pseudorandom) scrambling dynamics, the information from infalling entangled qubits can only be recovered from either the interior or the exterior of the black hole -- but never from both places at the same time. In the area of quantum cryptography, our game helps us construct succinct unclonable encryption schemes from the existence of pseudorandom unitaries, thereby, for the first time, bridging the gap between "MicroCrypt" and unclonable cryptography. The technical contribution of this work is a tight analysis of Haar cloning games which requires us to overcome many long-standing barriers in our understanding of cloning games. Answering these questions provably requires us to go beyond existing methods (Tomamichel, Fehr, Kaniewski and Wehner, New Journal of Physics 2013). In particular, we show a new technique for analyzing cloning games with respect to binary phase states through the lens of binary subtypes, and combine it with novel bounds on the operator norms of block-wise tensor products of matrices.

翻译：不可克隆原理在量子信息与密码学中具有基础性地位。遵循通过交互式游戏视角研究量子力学现象的长期传统，Broadbent与Lord（TQC 2020）形式化了克隆游戏，以在不可克隆加密方案的框架下定量刻画不可克隆性。本文的概念性贡献在于提出了一种新颖且自然的哈尔克隆游戏概念，并给出其两项应用。在黑洞物理领域，我们的游戏揭示：在具有哈尔随机（或伪随机）置乱动力学的理想化黑洞模型中，坠入黑洞的纠缠量子比特信息仅能从黑洞内部或外部恢复——而无法同时从两地获取。在量子密码学领域，该游戏帮助我们基于伪随机酉算子的存在性构建简洁的不可克隆加密方案，从而首次在"微密码学"与不可克隆密码学之间架起桥梁。本文的技术贡献在于对哈尔克隆游戏给出了紧致分析，这要求我们克服理解克隆游戏时长期存在的诸多障碍。严格回答这些问题需要超越现有方法（Tomamichel、Fehr、Kaniewski与Wehner，New Journal of Physics 2013）。特别地，我们提出了一种通过二元子类型视角分析基于二相态克隆游戏的新技术，并将其与矩阵分块张量积算子范数的新颖界相结合。