通过量子反馈实现多体动力学不确定关系中的海森堡标度
Heisenberg Scaling in Many-Body Kinetic Uncertainty Relation via Quantum Feedback
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中文总结 AI 辅助
研究量子设备计数可观测量精度的提升问题，通过对超辐射自旋系综应用量子反馈，实现计数精度的海森堡\(1/N^2\)标度，论证了反馈可将集体耗散转化为提升计数精度的资源。
中文摘要 AI 辅助
精度是量子设备的核心品质因数，量子时钟性能取决于计数事件稳定性。动力学不确定关系对计数可观测量精度设基本限制。多体效应虽有望提升性能，但计数精度能提升多少尚不明。量子计量中，海森堡标度指估计方差随粒子数\(N\)按\(1/N^2\)抑制。本文提出通过对超辐射自旋系综应用量子反馈实现此标度的协议。超辐射增强活动是瞬态的，只有由反馈控制时计数精度标度才可实现。通过多体动力学不确定关系和反馈修正平均场方程进行了分析论证，并经数值模拟验证。结果表明反馈可将集体耗散转化为海森堡标度计数精度的资源。
英文摘要
Kinetic uncertainty relations impose a fundamental constraint on counting precision by requiring large dynamical activity to suppress fluctuations. For $N$ independent constituents, the activity is additive and scales as $O(N)$, so the corresponding precision bound improves only as $O(1/N)$. A central question is whether many-body quantum systems can instead achieve Heisenberg scaling, with relative variance suppressed as $O(1/N^{2})$. Such scaling could enable substantially enhanced precision in quantum devices, including quantum clocks. Superradiance appears to provide a natural route because its collective emission activity can scale as $O(N^2)$. We show, however, that superradiance alone fails to achieve Heisenberg scaling because this enhanced activity is transient. We then demonstrate that jump-conditioned quantum feedback stabilizes the superradiant high-activity regime and converts this collective enhancement into Heisenberg scaling. We establish this mechanism analytically using a many-body kinetic uncertainty relation and mean-field analysis, and demonstrate through quantum-trajectory simulations that the actual relative counting fluctuation scales as $O(1/N^{2})$.
发表机构
- The University of Tokyo（东京大学）
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