发表机构
MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group; ELTE Eötvös Loránd University（MTA-ELTE“动量”可积量子动力学研究组; 布达佩斯罗兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带杨-巴克斯特门的一维砖墙电路，建立了算子施密特秩的多种增长上界，构造了反例证明部分情形下的指数增长，相关结果为算子纠缠增长问题提供了重要进展。
AI 中文摘要
我们研究一维砖墙电路中局域算子的算子纠缠，这类电路的两体门满足辫关系，在本研究中我们将这类门称为杨-巴克斯特门。我们对几类结构化的重叠杨-巴克斯特门建立了上界：证明了所有量子比特杨-巴克斯特门的算子施密特秩随时间保持一致有界；在任意局域维度下，由非退化杨-巴克斯特映射得到的置换门的算子施密特秩也随时间一致有界。还证明了对合双酉杨-巴克斯特门，以及由非退化杨-巴克斯特映射得到的置换门的任意相位修饰，其算子施密特秩最多呈多项式增长，这些结果分别对应算子纠缠的常数和对数上界。反之，我们构造了一个七态无双酉性的对合杨-巴克斯特门和一个单位点算子，其精确算子施密特秩呈指数增长，尽管对应的算子熵仍未确定。一般杨-巴克斯特情形下的纠缠增长问题仍未解决，所有证明和选定示例由ChatGPT 5.6 Sol构造。
英文摘要
We study the operator entanglement of local operators in one-dimensional brickwork circuits whose two-site gate satisfies the braid relation; throughout this work, we call such a gate a Yang--Baxter gate. We establish upper bounds for several structured, overlapping classes of Yang--Baxter gates. We show that the operator Schmidt rank remains uniformly bounded in time for all qubit Yang--Baxter gates and, in arbitrary local dimension, for permutation gates obtained from non-degenerate Yang--Baxter maps. We also show that it grows at most polynomially for involutive dual-unitary Yang--Baxter gates and for arbitrary phase dressings of permutation gates obtained from non-degenerate Yang--Baxter maps. These results imply, respectively, constant and logarithmic upper bounds on the operator entanglement. Conversely, we construct a seven-state involutive Yang--Baxter gate without dual unitarity and a one-site operator whose exact operator Schmidt rank grows exponentially, although the corresponding operator entropies remain undetermined. Entanglement growth in the general Yang--Baxter case remains open. All proofs and selected examples were constructed by ChatGPT 5.6 Sol.
Comments67 pages, v2: minor modifications
