我们通过将N级探针与玻色子和费米子环境耦合，并对其进行连续监测，研究了在玻色子和费米子环境中温度计的 fundamental 和 practical 精度极限。我们的发现表明，最终的精度极限，由Fisher信息量度，与N线性相关，相较于平衡温度计的 scaling 仅为 log² N 提供了指数级改进。对于固定的哈密顿结构，我们开发了一种最大似然估计策略，将观测到的连续监测探针轨迹映射为温度估计，其误差最小。通过优化所有可能的哈密顿结构，我们发现最优配置是一个有效的二能级系统，其中两个能级的退化性随N增加而增加，这与平衡温度计中基态非退化性形成鲜明对比。我们的结果具有实际意义。首先，连续监测在多个平台上实验上是可行的，并且考虑了探针的准备时间，这在其他方法如准备和重置中常被忽视。其次，线性缩放对偏离最优哈密顿结构的有效二能级结构的偏差具有鲁棒性。此外，这种鲁棒性还扩展到初始对温度的无知情况。因此，在全局估计问题中，即使没有自适应策略，线性缩放仍然保持不变。
英文摘要：
We investigate the fundamental and practical precision limits of thermometry in bosonic and fermionic environments by coupling an $N$-level probe to them and continuously monitoring it. Our findings show that the ultimate precision limit, quantified by the Fisher information, scales linearly with $N$, offering an exponential improvement over equilibrium thermometry, where the scaling is only $\log^2 N$. For a fixed Hamiltonian structure, we develop a maximum likelihood estimation strategy that maps the observed continuously monitored trajectories of the probe into temperature estimates with minimal error. By optimizing over all possible Hamiltonian structures, we discover that the optimal configuration is an effective two-level system, with both levels exhibiting degeneracy that increases with $N$-a stark contrast to equilibrium thermometry, where the ground state remains non-degenerate. Our results have practical implications. First, continuous monitoring is experimentally feasible on several platforms and accounts for the preparation time of the probe, which is often overlooked in other approaches such as prepare-and-reset. Second, the linear scaling is robust against deviations from the effective two-level structure of the optimal Hamiltonian. Additionally, this robustness extends to cases of initial ignorance about the temperature. Thus, in global estimation problems, the linear scaling remains intact even without adaptive strategies.
We discuss the problem of estimating a frequency via N-qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencie…
CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems
University of Rochester（罗切斯特大学）；Center for Coherence and Quantum Optics, University of Rochester（罗切斯特大学相干性与量子光学中心）；Institute for Quantum Studies, Chapman University（查普曼大学量子研究所）；Department of Chemistry, University of California, Berkeley（加州大学伯克利分校化学系）；Berkeley Center for Quantum Information and Computation（伯克利量子信息与计算中心）；Chapman University（查普曼大学）
Hypothesis testing with a continuously monitored quantum system
在贝叶斯分析中，特定候选参数支配量子系统演化的可能性取决于测量的结果，这反过来又会导致系统状态的测量反作用[M]。Tsang，Phys. Rev. Lett. 108，170502（2012）]。专门的两个候选假设的区别，我们研究的成就，连续监测的辐射发射的量子系统其次是一个最佳的投影测量其条件的最终状态。我们的辐射衰减的驱动二能级系统的研究表明，从光子计数和零差检测和发射器上的最终投影测量的最大信息之间的复杂的相互作用。我们比较的结果与理论预测的概率下限分配一个错误的假设，由任何组合测量系统及其辐射环境。
We put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. We show, in particular, that the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by the Holevo quantity. This, in turn, can be further split into an information gain rate and loss rate, which provide conditions for the existence of informational steady-states (ISSs), i.e. stationary states of a condition…
Fluctuation theorems allow one to make generalised statements about the behaviour of thermodynamic quantities in systems that are driven far from thermal equilibrium. In this article we use Crooks' fluctuation theorem to understand the entropy production of a continuously measured, zero-temperature quantum system; namely an optical cavity measured via homodyne detection. At zero temperature, if one uses the classical definition of inverse temperature $β$, then the entropy production becomes divergent. Our analysis shows that the entropy production can be well defined at zero temperature by con…
We consider the evolution of a quantum simple harmonic oscillator in a general Gaussian state under simultaneous time-continuous weak position and momentum measurements. We deduce the stochastic evolution equations for position and momentum expectation values and the covariance matrix elements from the system's characteristic function. By generalizing the Chantasri-Dressel-Jordan (CDJ) formalism (Chantasri et al.~2013 and 2015) to this continuous variable system, we construct its stochastic Hamiltonian and action. Action extremization gives us the equations for the most-likely readout paths an…
We study the problem of estimating a time dependent magnetic field by continuous optical probing of an atomic ensemble. The magnetic field is assumed to follow a stochastic Ornstein-Uhlenbeck process and it induces Larmor precession of the atomic ground state spin, which is read out by the Faraday polarization rotation of a laser field probe. The interactions and the measurement scheme are compatible with a hybrid quantum-classical Gaussian description of the unknown magnetic field, and the atomic and field variables. This casts the joint conditional quantum dynamics and classical parameter es…
Parameter Estimation in a Continuously Monitored Non-Markovian Quantum System
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）；University of Basel（巴塞尔大学）；Universidad de La Laguna（拉帕鲁纳大学）
The act of measuring a system has profound consequences of dynamical and thermodynamic nature. In particular, the degree of irreversibility ensuing from a non-equilibrium process is strongly affected by measurements aimed at acquiring information on the state of a system of interest: the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by clearly interpreted informational quantities. Building on a recently proposed collisional-model framework [G. T. Landi {\it et al.}, arXiv:2103.06247], we i…
Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Shanghai Research Center for Quantum Sciences and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学上海量子科学研究中心及中科院量子信息与量子物理卓越创新中心）；Institut für Theoretische Physik and IQST, Universität Ulm（乌尔姆大学理论物理研究所和IQST）；Department of Physics, Indian Institute of Technology (BHU), Varanasi（瓦拉纳西印度理工学院（贝拿勒斯）物理系）
We analyze the dynamics of entanglement in a paradigmatic noninteracting system subject to continuous monitoring of the local excitation densities. Recently, it was conjectured that the evolution of quantum correlations in such system is described by a semi-classical theory, based on entangled pairs of ballistically propagating quasiparticles and inspired by the hydrodynamic approach to unitary (integrable) quantum systems. Here, however, we show that this conjecture does not fully capture the complex behavior of quantum correlations emerging from the interplay between coherent dynamics and co…
We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases of distinct topological order. We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. In the presence of unitary dynamics, the two topologically distinct phases are separated by a region with sub-volume scaling of the entanglement entropy. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the t…
Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
Exact Hilbert-space ergodicity from continuous monitoring
Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Physics & State Key Laboratory of Surface Physics, Fudan University（复旦大学物理系与表面物理国家重点实验室）
Quantum noise scaling in continuously operating multiparameter sensors
ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学技术学院）；ICREA - Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究高级学院）
Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（南加州大学明思海电气与计算机工程系）；Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气与计算机工程系）；Department of Physics and Astronomy, University of Southern California（南加州大学物理与天文学系）
Fractal structure of multipartite entanglement in monitored quantum circuits
Smalley-Curl Institute, Rice University（莱斯大学斯马利-柯尔研究所）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文系）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）
Feedback-Enhanced Quantum Metrology and Clock Precision under Thermodynamic Uncertainty
Key Laboratory of Intelligent Optoelectronic Devices and Chips of Jiangsu Higher Education Institutions, School of Physical Science and Technology, Suzhou University of Science and Technology（江苏高校智能光电器件与芯片重点实验室，苏州科技大学物理科学与技术学院）；Advanced Technology Research Institute of Taihu Photon Center, School of Physical Science and Technology, Suzhou University of Science and Technology（太湖光子中心先进技术研究院，苏州科技大学物理科学与技术学院）；Department of Physics, Zhejiang Normal University（浙江师范大学物理系）
