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.
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.
Abstract Quantum entanglement lies at the heart of quantum information and quantum metrology. In quantum metrology, with a colossal amount of quantum Fisher information (QFI), entangled systems can be ameliorated to be a better resource scheme. However, noisy channels affect the QFI substantially. This research work seeks to investigate how QFI of N-qubit Greenberger-Horne-Zeilinger (GHZ) state is affected when subjected to decoherence channels: bit-phase flip (BPF) and generalize amplitude damping (GAD) channels, which can be induced experimentally. We determine the evolution under these channels, deduce the eigenvalues, and then derive the QFI. We found that when there is no interaction with the environment, the Heisenberg limit can be achieved via rotations along the z direction. It has been shown that in BPF channel, the maximal mean QFI of the N-qubit GHZ state ( Fˉmax F ¯ m a x ) dwindles as decoherence rate (p B ) increases due to flow of information from the system to the environment, until p B = 0.5, then revives to form a symmetric around p B = 0.5. Thus, p B > 0.5 leads to a situation where more noise yields more efficiency. We found that in GAD channel, at finite temperature, QFIs decay more rapidly than at zero temperature. Our results also reveal that QFI can be enhanced by adjusting the temperature of the environment.
Quantum metrology is a subject of studying quantum measurement and quantum statistical deduction, and the precision of parameter estimation can be enhanced by quantum properties. In general, the process of parameter estimation includes four steps:preparation of probe state, parameterization process, measurement, and data processing. Of these four steps, the preparation of probe state is the most crucial. However, in practical applications, in the process of preparing quantum probe state, the probe system will couple to its environment, which will inevitably cause the quantum properties of the probe system to deteriorate, and thus reducing the precision of quantum parameter estimation. The dynamics of quantum Fisher information (QFI) for W state and Greenberger-Horne-Zeilinger (GHZ) state have been studied in decoherence channels. Because W state and GHZ state have different entanglement properties, the studies of the dynamics of QFI for the superposition of W state and GHZ state are of practical significance in quantum metrology field. In this paper, the dynamics of QFIs for the superposition of W state and GHZ state in three typical decoherence channels (depolarization channel, amplitude damping channel and phase damping channel) are studied. In the four steps of quantum parameter estimation, our major attention is paid to the first step (i.e., the preparation of probe state). For comparison, the QFIs of different probe states are studied, with the other three steps fixed, i.e., all the probe states will undergo the same parameterization, measurement and estimation process. The parameterization process involved here is a quantum spin operation (specified by the spin rotation direction), which is chosen to maximize the QFI of the probe state. The initial probe states under consideration are the superpositions of W state and GHZ state of three-particle and five-particle systems, and the QFI dynamics of those probe states are studied in the three different typical decoherence channels. By using the operator-sum (Kraus) representation of those three typical decoherence channels, the QFI dynamics of the probe state can be analytically derived in three different decoherence channels. The results show that in the depolarization channel, the maximum QFI of the probe state decreases with the decoherence evolving to zero in the end; in the amplitude damping channel, the QFI of the probe state decreases to the minimum with the decoherence evolution and then increases to the shot noise limit; in the phase damping channel, the QFI of the probe state decreases with the evolution of decoherence, but the final stable value is not zero. Further analyses show that W state component of the superposition plays a role in resisting phase damping and the GHZ state component plays a role in resisting amplitude damping. These results can help us to choose the optimal probe state for maximizing the estimation precision in practice.
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.
Abstract Various quantum states have been suggested to realize high-precision measurement and quantum Fisher information (QFI) is one of the most important indicators to evaluate the performance. Here, we systematically investigate the QFI of an N-qubit maximal sliced (MS) state in different environments. In the ideal situation, we present the analytical QFI and it decays from N2 to (N − 1)2 as the parameter α changed from 0 to 1, which denotes the decreased metrological ability. In the amplitude damping channel, the variation trends of QFI with respect to p are similar and it decreases to the number of qubits N at p = 1, meaning the vanished entanglement superiority. However, it is different in the phase damping channel where with the increase of the number of qubits a turning point of QFI equal to N is found at p closing to 0.1. In the Ising-type interacting model, with the increasing interaction strength γ, the QFI with respect to α shows a crossover from decreasing to increasing. Particularly, at the critical point γ = 1, the QFI of an N-qubit MS state is found analytically equal to N2 and regardless of α. This indicates a great potential in achieving the Heisenberg-limited metrology and may shed some new light on quantum information science. PACS: 03.67.-a, 03.65.Ud
Abstract We investigate precision of phase estimation without and with decoherence using a non-Hermitian operation, i.e. parity-time ( ) symmetric operation. We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. Special attention is paid to the two schemes, i.e. pre-and post- symmetric operations, to show the performance of symmetric operation on QFI dynamics. By investigation, we find that pre- symmetric operator process could completely eliminate the effect of decoherence to improve the parameters estimation, while with the help of the post- symmetric operator process can potentially enhance and preserve the QFI by choosing appropriate non-Hermitian operator parameters.
We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for many-body wave functions known analytically in the occupation-number basis, systematic lower bounds to the QFI can be mapped onto expectation values over a classical probability distribution defined by the wave function amplitudes. This mapping enables efficient estimation via Markov-chain Monte Carlo sampling, with a computational cost that scales as a `slow' exponential (ebL with b≲0.6) and remains manageable for system sizes well beyond exact diagonalization. We specify this framework to Jastrow-Gutzwiller wave functions. We characterize their metrological content by identifying the observables that maximize the QFI and the corresponding scaling with L. Then, we analyze the QFI under three physically motivated noise channels: local dephasing, local amplitude damping, and global depolarizing. We compare polynomial and Krylov-based lower bounds across these channels, relating their behavior to the effective rank of the noisy density matrix and to the structure of the operator generating the parameter encoding. The framework extends naturally to other analytically known wave functions and to a broader class of information-theoretic quantities beyond the QFI.