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arXiv:2501.05668 · Physical Review Applied

Enhanced quantum parameter estimation via dynamical modulation

Guohui Dong, Yao Yao

Published May 15, 2025• 3 citations
arXivHTMLPDF

Abstract

In quantum theory, the inescapable interaction between a system and its surroundings would lead to a loss of coherence and leakage of information into the environment. An effective approach to retain the quantum characteristics of the system is to decouple it from the environment. However, things get complicated in quantum parameter estimation tasks, especially when the unknown parameter originates from the environment. Here, we propose a general dynamical modulation scheme that enables the enhancement of estimation precision irrespective of the origin of the parameters to be estimated. Notably, beyond the capability of dynamically decoupling the system from the environment, our proposal can select the effective frequency of the system and in turn manipulate the dynamics of the system, such as the steady-state probability and the decay rate, which are sensitive to the bath parameter. Therefore, the quantum Fisher information is dramatically increased, leading to superior estimation precision. Specifically, we elucidate the effectiveness of our proposal with prototypical examples of the Ramsey spectroscopy and quantum thermometer. Our findings offer an alternative route to enhance the precision of quantum estimation processes and may have potential applications in diverse branches of quantum metrology.

DOI
10.1103/njh2-4jwf

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In quantum theory, the inescapable interaction between a system and its surroundings would lead to a loss of coherence and leakage of information into the environment. An effective approach to retain the quantum characteristics of the system is to decouple it from the environment. However, things get complicated in quantum parameter estimation tasks, especially when the unknown parameter originates from the environment. Here, we propose a general dynamical modulation scheme that enables the enhancement of estimation precision irrespective of the origin of the parameters to be estimated. Notably, beyond the capability of dynamically decoupling the system from the environment, our proposal can select the effective frequency of the system and in turn manipulate the dynamics of the system, such as the steady-state probability and the decay rate, which are sensitive to the bath parameter. Therefore, the quantum Fisher information is dramatically increased, leading to superior estimation precision. Specifically, we elucidate the effectiveness of our proposal with prototypical examples of the Ramsey spectroscopy and quantum thermometer. Our findings offer an alternative route to enhance the precision of quantum estimation processes and may have potential applications in diverse branches of quantum metrology.
Abstract High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modeled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe can dramatically increase the maximum accuracy bound of low-temperatures estimation, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error bound at low temperatures in conventional quantum thermometry, periodic modulation of the probe allows for low-temperature thermometry with temperature-independent relative error bound. The proposed approach may find diverse applications related to precise probing of the temperature of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.
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We consider a thermometer modelled by a dynamically-controlled multilevel quantum system in contact with a bath. Periodic modulation of the energy level spacings of our quantum thermometer enables us to dramatically increase the accuracy of temperature estimation. As opposed to the diverging relative error near the absolute zero obtained in conventional thermometers, our control scheme enables high precision temperature estimation arbitrarily close to the absolute zero, by maximizing its quantum Fisher information. Alternatively, dynamical control may allow for high-precision measurement of multiple temperatures.
Accurately characterizing the properties of structured reservoirs is a key challenge in quantum systems and is of great importance for advances in quantum metrology and sensing. In this work, we employ a two-level system (qubit) as a probe, which is coupled to a structured reservoir consisting of an ancilla qubit and a Markovian environment modeled as a thermal bath. By exploiting non-Markovian dynamics, we systematically investigate the effectiveness of different interaction types between the probe and ancilla for estimating critical parameters, including temperature, ancilla frequency, and system-bath coupling strength. We quantify the precision of parameter estimation using quantum Fisher information (QFI) and analyze the system dynamics in both transient and steady-state regimes. Our findings demonstrate that non-Markovianity substantially enhances parameter estimation in the transient regime, with specific interactions facilitating sustained information backflow and yielding higher QFI values. However, the performance of these interactions is contingent on the parameter under estimation and the operational regime. For instance, certain interactions become prominent in the transient regime but exhibit diminished utility in the steady state, whereas others maintain their effectiveness even at equilibrium. These results stress the importance of judiciously selecting interactions adapted to specific estimation objectives and operational regimes.
We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. ``Heisenberg scaling''). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.
Abstract The quantum Fisher information (QFI) plays a key role in quantum metrological scenarios, and can be enhanced by certain entanglement protocols. In this work, we focus on the maximal mean QFI for L qubits, and study how a dynamical decoupling scheme rescues the entanglement-assisted QFI, which would be rapidly damaged by decoherence without such a scheme. We found that the square-wave modulation for the transition frequency of the qubit can be settled in a recursive transfer matrix form thus both periodic and random pulse sequences can be investigated exactly by assuming that the spectral density of the reservoir is Lorentzian. Considering the Greenberger–Horne–Zeilinger state as an initial state of L qubits imbedded in the independent damping channels, the use of additional square-wave pulse sequences allows the Heisenberg scaling to be restored for parameterestimation precision. How to optimize the pulse parameters with certain pulse energies should be carefully treated. The analyzability of the modulated damping dynamics may provide a potential start point for defeating decoherence in quantum information processing.