接触阶决定纠缠级联的起始
Contact order governs the onset of entanglement cascades
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中文总结 AI 辅助
本文提出接触阶$m_\star$决定纠缠级联的起始，通过时间有序递归计算，并给出三量子比特和三模玻色子例子验证。
中文摘要 AI 辅助
纠缠速率描述直接纠缠通道，但当该通道被禁止时不提供任何信息。对于有限维解析纯态动力学，我们证明真正的$(n+1)$部分纠缠的起始由物理轨迹与$S|E$乘积流形之间的接触阶$m_\star$决定。它是任何乘积曲线无法重现的第一个泰勒阶，或等价地，是与乘积流形的Fubini-Study距离的第一个非零阶。我们推导出一个时间有序递归，该递归移除曲率引起的运动学项，并从$H(t)$的泰勒系数计算$m_\star$。这提供了纠缠级联的几何描述，其中新子系统只有在一次或多次相互作用步骤之后才能加入多部分纠缠。一个对称保护的三量子比特模型实现了$m_\star=2$，一个三模玻色子例子表明，即使两个新形成的约化对保持可分离，真正的三部分纠缠也可以出现。
英文摘要
Entangling rates describe a direct entangling channel, but give no information when that channel is forbidden. For finite-dimensional analytic pure-state dynamics, we show that the onset of genuine $(n+1)$-partite entanglement is determined by the contact order $m_\star$ between the physical trajectory and the $S|E$ product manifold. It is the first Taylor order that cannot be reproduced by any product curve, or equivalently the first nonvanishing order of the Fubini--Study distance from the product manifold. We derive a time-ordered recursion that removes curvature-induced kinematic terms and computes $m_\star$ from the Taylor coefficients of $H(t)$. This provides a geometric description of an entanglement cascade, in which new subsystems can join multipartite entanglement only after one or more interaction steps. A symmetry-protected three-qubit model realizes $m_\star=2$, and a three-mode bosonic example shows that genuine tripartite entanglement can arise even when the two newly formed reduced pairs remain separable.
发表机构
- Kyushu University（九州大学）
- Quantum and Spacetime Research Institute, Kyushu University（九州大学量子与时空研究所）
- Kobe University（神户大学）
机构由 AI 辅助整理，请以论文原文为准。
