We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k-body Hamiltonian and p-body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N^{-[k-(p/2)]}, surpassing the shot-noise limit for 2k>p+1. Metrology equivalence between initial product states and maximally entangled states is established for p≥1. We further show that one can estimate the system-environment coupling parameter with precision N^{-(p/2)}, while many-body decoherence enhances the precision to N^{-k} in the noise-amplitude estimation of a fluctuating k-body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.
We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k-body Hamiltonian and p-body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N^{-[k-(p/2)]}, surpassing the shot-noise limit for 2k>p+1. Metrology equivalence between initial product states and maximally entangled states is established for p≥1. We further show that one can estimate the system-environment coupling parameter with precision N^{-(p/2)}, while many-body decoherence enhances the precision to N^{-k} in the noise-amplitude estimation of a fluctuating k-body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.
We study the performance of initial product states of n-body systems in generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body $(k\ensuremath{\ll}n)$ Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as 1/nk, and for initial product states, it scales as $1/{n}^{k\ensuremath{-}1/2}$. We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian (k=2), implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the $O({n}^{\ensuremath{-}3/2})$ scaling for k=2; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the $O({n}^{\ensuremath{-}3/2})$ sensitivity scaling for initial product states.
Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals encoded through Markovian Lindblad dynamics, allowing for arbitrary quantum control and noiseless ancillae. Although Markovianity enforces standard-quantum-limit scaling with sensing time T, our bounds reveal Heisenberg-type scaling in the number of dissipative channels, R: when the stochastic signal exhibits high-rank correlations across the R channels and the probe is entangled, the average variance (per parameter) scales no better than Ω(1/(TR2)). For collective k-body dissipation, R=Θ(Nk), signifying super-Heisenberg scaling with the system size N. We further show that, when the unknown parameters enter through the dissipative eigenrates, a Rapid Prepare-and-Measure (RPM) protocol that tracks many distinct quantum jumps in parallel attains these limits. In this regime, the estimation problem reduces to a multi-Poisson counting model, providing a conceptually clean route to optimal quantum noise metrology. We illustrate the breadth of the framework with applications to networked noise metrology, collective many-body dissipation, learning Pauli noise, and subdiffraction quantum imaging.
Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we establish a link between the bound on the growth of the quantum Fisher information and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems. We show that for initial separable states, despite the use of local many-body interactions, the precision cannot surpass the shot noise limit at all times. This conclusion also holds for an initial state that is the nondegenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling.
We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.
Estimation of physical parameters is essential in almost any part of science and technology. The enhancement of performance in this task (e.g. beating the standard classical shot-noise limit) using available physical resources is a major goal in metrology. Quantum metrology in closed systems has indicated that entanglement in such systems may be a useful resource. However, whether in open quantum systems such enhancements may still show up is not yet fully understood. Here, we consider a dissipative (open) quantum system of identical particles in which a parameter of the open dynamics itself is to be estimated. We employ a recently developed dissipative quantum metrology framework, and investigate whether the entanglement produced in the course of the dissipative dynamics may help the estimation task. Specifically, we show that, even in a Markovian dynamics in which states become less distinguishable in time, at small enough times the entanglement generated by the dynamics may offer some advantage over the classical shot-noise limit.
Accurate parameter estimation is a central task in quantum metrology and sensing, where quantum resources can provide precision beyond classical limits. In realistic settings, however, system-environment interactions lead to decoherence, reducing these strategies to their classical counterparts. Noise is typically classified as Markovian or non-Markovian, with the latter often preserving quantum coherence longer and thus supporting better metrological performance. Still, the absence of noise is generally considered ideal. In this work, we uncover a striking reversal: certain non-Markovian environments not only outperform Markovian ones - including their quantum Cramér-Rao bounds - but can also surpass the entirely noiseless case. We demonstrate these findings numerically for an all-optical setup, which is experimentally feasible and can be extended to other physical platforms. In general, our results open new avenues for noise-assisted quantum metrology beyond conventional limits.