用多体探针达到基态计量学的极限
Reaching the Limits of Ground-State Metrology with Many-Body Probes
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中文总结 AI 辅助
本文研究了多体探针达到基态计量学静态与动力学极限的条件，揭示了短程系统需临界指数满足ν(d+z)=1，长程系统可在有隙时最优，并提出了局部绝热协议实现最优制备，为设计极限精度传感器奠定理论基础。
中文摘要 AI 辅助
我们研究了使用具有短程或长程相互作用的多体探针达到基态计量学终极极限的物理条件，即通过对N体哈密顿量的基态进行测量来估计未知参数θ。我们刻画了饱和量子Fisher信息F_θ的两个基本极限的条件：静态基态界F_θ ≲ N^2/Δ^2，其中Δ是谱隙；以及动力学海森堡极限F_θ ≲ N^2 τ^2，其中τ是总协议持续时间。为了饱和静态极限，我们认为短程相互作用系统需要谱隙随N闭合。在二阶量子临界点，这导致对临界指数的普适条件ν(d+z)=1，该条件可以被任意接近，正如我们在XXZ链中所示；一阶跃迁处的类猫基态提供了达到静态最优性的替代途径。相反，我们发现全对全相互作用模型即使在有隙区域也能达到最优性。此外，达到动力学界与基态制备时间密切相关；我们证明其最优的逆隙轮廓可以通过局部绝热协议获得。通过分析典型系统——横场伊辛链、XXZ链、压缩哈密顿量和双模玻色-哈伯德模型——我们确定了能够接近这两个极限的特定多体探针。总的来说，我们的结果为设计在量子精度终极极限下运行的（局部）多体基态传感器提供了理论基础。
英文摘要
We investigate the physical requirements to reach the ultimate limits of ground-state metrology -- i.e., the estimation of an unknown parameter $θ$ of an $N$-body Hamiltonian via measurements on its ground state -- using many-body probes featuring either short-range or long-range interactions. We characterize the conditions to saturate two fundamental limits of the quantum Fisher information $F_θ$: the static ground-state bound $F_θ\lesssim N^2/Δ^2$, where $Δ$ is the spectral gap, and the dynamical Heisenberg limit $F_θ\lesssim N^2 τ^2$, where $τ$ is the total protocol duration. To saturate the static limit, we argue that short-range interacting systems require a spectral gap that closes with $N$. At second-order quantum critical points this leads to a universal condition on the critical exponents, $ν(d+z)=1$, which can be approached arbitrarily closely, as we show for the XXZ chain; cat-like ground states at first-order transitions provide an alternative route to static optimality. In contrast, we find that all-to-all interacting models can achieve optimality even in gapped regimes. Furthermore, reaching the dynamical bound is tightly related to the ground-state preparation time; we demonstrate that its optimal, inverse-gap profile can be obtained via local adiabatic protocols. By analyzing paradigmatic systems -- the transverse-field Ising chain, the XXZ chain, a squeezing Hamiltonian, and the two-mode Bose-Hubbard model -- we identify specific many-body probes capable of approaching both limits. Overall, our results provide a theoretical basis for the design of (local) many-body ground-state sensors operating at the ultimate limits of quantum precision.
发表机构
- Universitat Autònoma de Barcelona（巴塞罗那自治大学）
- Technische Universität Wien（维也纳工业大学）
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
- Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
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