Abstract This letter shows how incoherent dynamics can lead to metrological advantages in quantum sensing. The results rely on the fact that incoherent dynamics lead to an additive contribution to the quantum Fisher information about time. Such an additive contribution can reduce the error of optimal estimation protocols, as implied by the quantum Cramér–Rao bound. I characterize regimes in which the estimation of a time interval or a frequency is enhanced by decoherence, thereby identifying cases in which incoherent dynamics serve as a metrological resource. The decoherence processes that yield enhanced precision of quantum sensors can be engineered by randomized Hamiltonian dynamics. I illustrate the results with protocols that display improved sensing of time intervals or global fields by qubit and photonic sensors. Enhanced precision of time intervals is achieved with Hamiltonians that include randomized global parameters. Enhanced precision in field estimation is obtained by randomized sensing times.
Abstract This letter shows how incoherent dynamics can lead to metrological advantages in quantum sensing. The results rely on the fact that incoherent dynamics lead to an additive contribution to the quantum Fisher information about time. Such an additive contribution can reduce the error of optimal estimation protocols, as implied by the quantum Cramér–Rao bound. I characterize regimes in which the estimation of a time interval or a frequency is enhanced by decoherence, thereby identifying cases in which incoherent dynamics serve as a metrological resource. The decoherence processes that yield enhanced precision of quantum sensors can be engineered by randomized Hamiltonian dynamics. I illustrate the results with protocols that display improved sensing of time intervals or global fields by qubit and photonic sensors. Enhanced precision of time intervals is achieved with Hamiltonians that include randomized global parameters. Enhanced precision in field estimation is obtained by randomized sensing times.
Frequency estimation, a cornerstone of quantum metrology, has been significantly enhanced by advanced quantum sensing strategies. However, most protocols rely either on static or time-independent encoding mechanisms, inherently limiting their achievable precision scaling, or on control strategies requiring changing the Hamiltonian and/or implementing feedback mechanisms. To overcome this, we investigate a simpler dynamical encoding protocol where the quantum oscillator is driven by a general continuous temporal frequency modulation Ω(t)=ω0f(t). We analytically demonstrate that for a given modulation profile f(t) and its corresponding time-integral F(t), the quantum Fisher information (QFI) scales as O(F(t)2). This enhancement stems from the fact that temporal encoding fundamentally alters the mechanism of dynamical phase accumulation. Crucially, when evaluated under the energy and evolution-time constraints, this framework reveals a genuine precision enhancement over the conventional time-independent baseline. By analyzing explicit polynomial and exponential modulations, we establish that arbitrary precision scaling can be deterministically engineered, with ultimate bounds that are asymptotically saturable via optimal homodyne detection. Our framework provides a universal paradigm for exploiting time-dependent quantum control in next-generation sensors.
Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable systems, focusing on two complementary strategies to mitigate decoherence: Hamiltonian engineering and the exploitation of non-Markovian dynamics. By embedding squeezing directly into the system Hamiltonian, we show that the quantum Fisher information (QFI) may acquire a tunable higher-order time dependence, leading to enhanced sensitivity in the short-time regime. Moving beyond the Markovian approximation, we employ the quantum Brownian motion model to demonstrate that structured environments with finite memory can induce information backflow, temporarily restoring and even improving estimation precision relative to the unitary limit. We further assess the achievability of these bounds via Gaussian measurements, identifying regimes where homodyne, heterodyne, and optimized general-dyne measurements saturate the QFI, and noting that stronger squeezing widens the gap, potentially requiring non-Gaussian measurement strategies. Our results establish that jointly tailoring system Hamiltonian and environmental memory offers a viable route toward robust quantum-enhanced frequency estimation in open systems.
We find that a quantum device having an accessory involving precision measurement can have an enhancement of its metrological precision in estimating an unknown parameter of the quantum system by insertion of glassy disorder, accidental or engineered. We clearly mention how an unbiased estimator can also be identified in a disordered situation and how the precision thereof can be bounded by the quantum Cr\'amer-Rao inequality. We compare the Fisher information-based lower bound of the minimum standard deviation of an unbiased estimator, in the presence of glassy disorder in the system, with the same of an ideal, viz. disorder-free, situation. The phenomenon can boost the efficiency of certain measuring devices, such as atomic clocks. The precision of these clocks, when measuring time, hinges on the precise determination of the frequency of a two-level atom. In cases where impurities are present in the atom, and can be modeled as a disorder parameter, it is possible for the measurement of frequency to be more accurate than in an ideal, disorder-free scenario. Moreover, disorder insertion can reduce the requirement of entanglement content of the initial probes, which are copies of two-qubit states, along with providing a disorder-induced enhancement.
Abstract Entanglement is one of the key ingredients for enhancing the measurement precision of quantum sensors. Generally, there is a trade-off between state preparation and sensing within a limited coherence time. To fully exploit temporal resources, concurrent entanglement generation and sensing with designed sequence of rotations are proposed. Based on twist-and-turn dynamics, modulated rotations along only one axis may be sufficient to drive the state to the optimal one for tiny estimated parameter. However, when the estimated parameter is not tiny, it may impact the evolved state and hence degrade the final measurement precision. Here, we introduce another modulated rotations along different axis and find out the optimal control sequences by means of machine optimization. The optimal measurement precision bounds become independent on the estimated parameter, which improves the dynamic range of the machine designed sensors. Particularly, by optimizing the interaction strength for different particle number and the time-modulated rotations along two different axes via machine optimization, the Heisenberg-limited precision scaling can be attained. Our work points out a way for designing optimized quantum-enhanced metrology protocols, which is promising for developing practical quantum sensors.
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We demonstrate that both of these constraints can be overcome in quantum chaotic sensors. Crucially, we establish that even in the presence of partial measurement accessibility, chaotic dynamics enables initial unentangled states to exhibit Heisenberg scaling of the quantum Fisher information, Iα with time. In the weakly chaotic regime, we identify spin-coherent states placed at the edge of the regular islands in the mixed classical phase space as optimal initial states for enhanced sensitivity. On the other hand, in the strongly chaotic regime, Iα is insensitive to the choice of the initial state. Notably, quantum-enhanced sensitivity is achieved even when a very low fraction (∼5%) of the qubits are accessible. These results establish quantum chaos as a robust resource for quantum-enhanced sensing under realistic accessibility constraints on accessibility.
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cramèr–Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are situations in classical and quantum metrology where the unknown parameter of interest, besides determining the state of the probe, is also influencing the operation of the measuring devices, e.g. the range of possible outcomes. In those cases, nonregular statistical models may appear, for which the Cramèr–Rao theorem does not hold. In turn, the achievable precision may exceed the Cramèr–Rao bound, opening new avenues for enhanced metrology. We focus on quantum estimation of Hamiltonian parameters and show that an achievable bound to precision (beyond the Cramèr–Rao) may be obtained in a closed form for the class of so-called controlled energy measurements. Examples of applications of the new bound to various estimation problems in quantum metrology are worked out in some details.