标题： 自由独立性和双幺正量子电路中的非相交分划格 显示英文标题

标题： Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits

摘要： 我们通过评估所有的$2k$-点出-of-时间有序关联函数来研究双单位量子电路的混沌动力学细节。 对于一般的电路类，通过将关联函数写为一类量子通道的收缩，我们证明了它们的指数衰减。 这意味着时间上分离的局域算符接近自由独立性。 在此过程中，我们为双单位量子电路开发了一种复制技巧，这可能在自身范围内有用且有趣。 我们通过非交叉划分格中的路径来分类复制转移矩阵的相关特征态，这些组合对象是自由概率论的核心。 有趣的是，即使对于没有随机性和小的现场希尔伯特空间维数的系统，非交叉格也会出现。 显示英文摘要

摘要： We investigate details of the chaotic dynamics of dual-unitary quantum circuits by evaluating all $2k$-point out-of-time-ordered correlators. For the generic class of circuits, by writing the correlators as contractions of a class of quantum channels, we prove their exponential decay. This implies that local operators separated in time approach free independence. Along the way, we develop a replica trick for dual-unitary circuits, which may be useful and of interest in its own right. We classify the relevant eigenstates of the replica transfer matrix by paths in the lattice of noncrossing partitions, combinatorial objects central to free probability theory. Interestingly, the noncrossing lattice emerges even for systems without randomness and with small onsite Hilbert space dimension.