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].

翻译：我们为子空间共设状态建立了一个强大的一夫一妻制缠绕属性, 这些属性是矢量在 $\ mathbb{F ⁇ 2 ⁇ n$ 线性子空间的一致叠加, 曾经对它应用过一个一次性的量子垫。 这个属性最近被[ 哥拉登戈、 刘刘、 刘 和赞德利、 加密托' 21] 所推断, 并展示了对不可调和的解密和伪体功能的复制保护的应用。 我们提供了两种证据, 一种直接遵循原始纸张的方法, 另一种则使用来自[ Vidick 和张, Eurocrypt'20] 的观测, 将分析减少到基于 BB'84 状态的更简单的单项游戏。 这两种证据最终都依赖于在 [Tomamiheel、 Fehr、 Kaniewski 和 Wehner, 新物理杂志 13] 中引入的同一证据技术。