发表机构
University of Tübingen; University of Cambridge（蒂宾根大学; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明局部耗散可恢复玻色-哈伯德系统的算子范数Lieb-Robinson界，通过正则化高占据位点实现几乎弹道式传播界，并推广至猫码耗散，支持局部绝热近似及高效量子模拟。
AI 中文摘要
封闭玻色晶格系统通常不允许算子范数Lieb-Robinson界对初始状态一致成立。原因是信息传播速度可能随局部玻色子占据数增长，而该占据数可能宏观巨大。在此，我们证明局部耗散恢复了算子范数Lieb-Robinson界。我们考虑由Lindblad算子描述的耗散玻色-哈伯德模型，该模型具有格点上的$\ell$光子损失，$\ell>2$，对于我们的主要结果，我们建立了一个几乎弹道式的Lieb-Robinson界。耗散迅速耗尽高占据位点，从而在局部粒子矩的Sobolev型尺度上正则化状态。由此产生的矩界在时间趋近于零时发散，但在足够低的阶数下在零附近保持可积。我们将这些思想扩展到处理猫码耗散，并且对于码空间中的初始状态，我们证明了一个对总体积一致的局部绝热近似。进一步的结果包括局部信道近似、热力学极限和高效数字量子模拟。关键在于，这些应用现在对输入状态一致可用，如同量子自旋系统，但与封闭玻色-哈伯德系统形成对比。
英文摘要
Closed bosonic lattice systems do not generally admit operator norm Lieb--Robinson bounds uniformly in the initial state. The reason is that the information propagation velocity can grow with the local boson occupancy, which can be macroscopically large. Here, we show that local dissipation restores an operator-norm Lieb--Robinson bound. We consider the dissipative Bose--Hubbard model described by a Lindbladian operator with on-site $\ell$-photon loss, $\ell>2$ and, for our main result, we establish an almost-ballistic Lieb-Robinson bound. Dissipation rapidly depletes highly occupied sites, thus regularizing the state on the Sobolev-type scale of local particle moments. The resulting moment bounds diverge as time approaches zero but remain integrable near zero at sufficiently low orders. We extend these ideas to treat cat-code dissipation and, for initial states in the code space, we prove a local adiabatic approximation uniform in the total volume. Further consequences include local channel approximation, a thermodynamic limit, and efficient digital quantum simulation. The point is that these applications are now available \textit{uniformly in the input state}, as for quantum spin systems, but in contrast to closed Bose--Hubbard systems.
