发表机构
Institut für Theoretische Physik, Universität Tübingen; School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham（蒂宾根大学理论物理研究所; 诺丁汉大学物理与天文学院及量子非平衡系统数学与理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用Keldysh路径积分推导驱动-耗散多体系统量子Fisher信息的半经典表达式，并在三个系统中验证其有效性，为量子增强传感提供新工具。
AI 中文摘要
驱动-耗散多体量子系统可用于量子增强传感协议。在此类协议中，非经典关联可能使测量精度超越标准量子极限。评估这种量子优势的相关度量是量子Fisher信息（QFI）。在多体环境中，计算QFI具有挑战性，因为它需要完整系统-环境态的知识。在此，我们采用一种特别适用于具有多自由度的系统的场论方法。具体而言，我们证明QFI可以与Keldysh路径积分相关联。这一途径导出了QFI的半经典表达式，该表达式通过对所谓的量子场进行受控展开而获得。我们在三个复杂度递增的系统上对该框架进行了基准测试：驱动-耗散谐振子、边界时间晶体（在大系统尺寸下变得半经典）以及二维集体发射原子阵列。我们评估了半经典描述在哪些参数区域内成立，并能够访问超出精确方法能力范围的系统尺寸。
英文摘要
Driven-dissipative many-body quantum systems can be exploited in quantum enhanced sensing protocols. Here, non-classical correlations may allow one to reach a measurement precision that surpasses the standard quantum limit. The relevant figure of merit for assessing such quantum advantage is the quantum Fisher information (QFI). In a many-body setting its computation is challenging as it requires knowledge of the full system-environment state. Here we make use of a field-theoretical approach, which is particularly well suited for systems with many degrees of freedom. In particular, we show that the QFI can be linked to a Keldysh path-integral. This route leads to a semiclassical expression of the QFI, which is obtained through a controlled expansion in the so- called quantum fields. We benchmark the framework on three systems of increasing complexity: the driven-dissipative harmonic oscillator, the boundary time crystal - which becomes semiclassical at large system sizes - and a two-dimensional array of collectively emitting atoms. We assess in which parameter regimes the semiclassical description holds and gives access to system sizes beyond the reach of exact methods.
