We establish a strong monogamy-of-entanglement property for subspace coset states, which are uniform superpositions of vectors in a linear subspace of $\mathbb{F}_2^n$ to which has been applied a quantum one-time pad. This property was conjectured recently by [Coladangelo, Liu, Liu, and Zhandry, Crypto'21] and shown to have applications to unclonable decryption and copy-protection of pseudorandom functions. We present two proofs, one which directly follows the method of the original paper and the other which uses an observation from [Vidick and Zhang, Eurocrypt'20] to reduce the analysis to a simpler monogamy game based on BB'84 states. Both proofs ultimately rely on the same proof technique, introduced in [Tomamichel, Fehr, Kaniewski and Wehner, New Journal of Physics '13].

中文翻译：

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子空间陪集状态的一夫一妻纠缠博弈

我们为子空间陪集状态建立了强大的一夫一妻纠缠性质，这些状态是向量在 $\mathbb{F}_2^n$ 的线性子空间中的均匀叠加，该子空间已应用量子一次性垫。最近 [Coladangelo, Liu, Liu 和 Zhandry, Crypto'21] 推测了此属性，并证明其可应用于伪随机函数的不可克隆解密和复制保护。我们提出了两个证明，一个直接遵循原始论文的方法，另一个使用来自 [Vidick and Zhang, Eurocrypt'20] 的观察将分析简化为基于 BB'84 状态的更简单的一夫一妻制游戏。两种证明最终都依赖于 [Tomamichel、Fehr、Kaniewski 和 Wehner，New Journal of Physics '13] 中介绍的相同证明技术。