We present a scheme to enhance the precision of parameter estimation (PPE) in noisy systems by employing dynamical decoupling pulses. An exact analytical expression for the estimation precision of an unknown parameter is obtained by using the transfer matrix and time-dependent Kraus operators. We show that the PPE in noisy systems can be preserved in the Heisenberg limit by control of the dynamical decoupling pulses. It is found that a larger number of pulses and longer reservoir correlation time can greatly protect the PPE.
We present a scheme to enhance the precision of parameter estimation (PPE) in noisy systems by employing dynamical decoupling pulses. An exact analytical expression for the estimation precision of an unknown parameter is obtained by using the transfer matrix and time-dependent Kraus operators. We show that the PPE in noisy systems can be preserved in the Heisenberg limit by control of the dynamical decoupling pulses. It is found that a larger number of pulses and longer reservoir correlation time can greatly protect the PPE.
We study the dephasing-assisted parameter estimation precision (PEP) enhancement in an atom interferometer with dynamical decoupling (DD) pulses. Through calculating the spin squeezing (SS) and the quantum Fisher information, we find that dephasing noise can improve PEP by inducing SS, and the DD pulses can maximize the improvement. It is indicated that when using the DD pulse the dephasing-induced SS can reach the limit of ``one-axis twisting'' model ${\ensuremath{\xi}}^{2}\ensuremath{\simeq}{N}^{\ensuremath{-}2/3}$ with ${\ensuremath{\xi}}^{2}$ being the SS parameter and N the number of atoms. In particular, we find that the DD pulses can amplify the dephasing-induced quantum Fisher information by a factor of $\ensuremath{\simeq}N/2$ compared with the noise-free case, which means that under the control of DD pulses, the dephasing noise can enhance the precision of parameter estimation to the scale of 2/N, the same scale of the Heisenberg limit (1/N).
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.
We present a useful method to enhance parameter estimation precision (PEP) in quantum systems by mitigating the detrimental effects of decoherence and environmental noise. We consider a theoretical model featuring a single qubit coupled to a zero-temperature bosonic reservoir with a Lorentzian spectral density, augmented by non-interacting auxiliary qubits. Our analysis spans both Markovian and non-Markovian dynamical regimes, demonstrating that auxiliary qubits effectively preserve PEP by stabilizing quantum Fisher information (QFI) and local quantum uncertainty (LQU), key metrics for precise PEP and quantum correlation. Additionally, detuning between the qubit and reservoir frequencies serves as a tunable parameter to further reduce decoherence. Employing the Kraus operator formalism, we reveal how these strategies create a decoherence-free subspace, offering a passive and scalable approach to protect quantum measurements. The results highlight significant potential for improving quantum metrology and information processing technologies in noisy environments, providing practical insights for advancing quantum system performance.
Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.
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.
Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD and its extension, concatenated DD, for scaling up its power. The qualitative conclusions from our analysis of these two schemes nevertheless apply to other DD approaches. In the presence of noisy pulses, DD does not always mitigate errors. It does so only when the added noise from the imperfect DD pulses does not outweigh the increased ability in averaging away the original background noise. We present break-even conditions that delineate when DD is useful, and further find that there is a limit in the performance of concatenated DD, specifically in how far one can concatenate the DD pulse sequences before the added noise no longer offers any further benefit in error mitigation.