发表机构
Yau Mathematical Sciences Center, Tsinghua University（丘成桐数学科学中心，清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究模流纠缠熵中的不等式与正性，通过建立熵平衡、利用共形场论性质及Araki相对熵等，证明模纠缠偏移的相关性质并探讨其在AdS/CFT对应中的应用。
AI 中文摘要
模哈密顿量在量子信息论、量子场论以及AdS/CFT对应中发挥着重要作用。在本文中，我们研究一个特定的动力学设置：从参考态的约化密度矩阵的张量积出发，在参考态自身产生的模流下演化这个乘积态。随后我们研究给定区域纠缠熵的变化，将其称为模纠缠偏移（MES）。与在固定量子信道下的演化不同，这种模演化没有要求MES具有确定符号的通用原理。对于划分为子系统A和B的二分结构，我们建立了精确的熵平衡：A和B的MES之和等于沿轨道产生的互信息。因此，即使单个偏移可能为负，它们的总和也是非负的。然而，对于二维共形场论真空中的两个不相交区间，我们证明交换这两个区间的全局共形对合迫使两个MES相等。由此可得，每个MES在模流过程中都是非负的。我们既利用共形传输的正则化子证明了该结果，又根据Araki相对熵内在地证明了该结果。最后，我们将模流轨道与Connes上循环轨道等同起来，并讨论其在AdS/CFT对应中的可能应用。
英文摘要
The modular Hamiltonian plays an important role in quantum information theory, quantum field theory, and the AdS/CFT correspondence. In this paper, we study a specific dynamical setup: starting from the tensor product of the reduced density matrices of a reference state, we evolve this product state under the modular flow generated by the reference state itself. We then investigate the resulting change in the entanglement entropy of a given region, which we call the modular entanglement shift (MES). Unlike evolution under a fixed quantum channel, this modular evolution obeys no general principle requiring the MES to have a definite sign. For a bipartition into subsystems A and B, we establish an exact entropy balance: the sum of the MESs for A and B equals the mutual information generated along the orbit. Consequently, their sum is nonnegative, even though either individual shift may be negative. For two disjoint intervals in the vacuum of a two-dimensional conformal field theory, however, we prove that a global conformal involution exchanging the intervals forces the two MESs to be equal. It follows that each MES is nonnegative along the modular flow. We establish this result both using a conformally transported regulator and intrinsically in terms of Araki relative entropy. Finally, we identify the modular-flow orbit with a Connes cocycle orbit and discuss possible applications to the AdS/CFT correspondence.
Comments9 pages, 1 figure
