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Chinese Physics Letters

Dynamics of Quantum Fisher Information in Homodyne-Mediated Feedback Control

Li Chen, Dong Yan, Li-Jun Song, Shou Zhang

Published Mar 1, 2019• 9 citations
Publisher

Abstract

We investigate the quantum Fisher information (QFI) dynamics of a dissipative two-level system in homodyne-mediated quantum feedback control. The analytical results demonstrate that the maximum values and stable values of the QFI can be greatly enhanced via feedback control. The quantum feedback plays a more evident role in the improvement of classical Fisher information. The classical part can reach a high stable value, while the quantum part eventually decays to zero whatever the feedback parameter is .

DOI
10.1088/0256-307x/36/3/030302

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We investigate the quantum Fisher information (QFI) dynamics of a dissipative two-level system in homodyne-mediated quantum feedback control. The analytical results demonstrate that the maximum values and stable values of the QFI can be greatly enhanced via feedback control. The quantum feedback plays a more evident role in the improvement of classical Fisher information. The classical part can reach a high stable value, while the quantum part eventually decays to zero whatever the feedback parameter is .
Abstract A two-level atom interacting with a single-mode cavity is considered. The atom-cavity system is driven by a classical field with the homodyne-mediated feedback. The influences of the driving field and two types of the feedback on the precision of the phase estimation are investigated. The results show the quantum Fisher information (QFI) can be preserved by the homodyne-mediated feedback and the classical driving when the system parameters are suitable. In addition, the initial value of the relative phase greatly effects the QFI. Therefore, the phase estimation precision of the two-level atom can be enhanced, and the extent of the enhancement is decided by not only the driving frequency and the type of quantum feedback, but also the initial parameters of the two-level system.
Various schemes have been proposed to overcome the drawback of the decoherence on quantum-enhanced parameter estimation. Here we suggest an alternative method, quantum feedback, to enhance the parameter precision of optimal quantum estimation of a dissipative qubit by investigating its dynamics of quantum Fisher information. We find that compared with the case without feedback, the quantum Fisher information of the dissipative qubit in the case of feedback has a large maximum value in time evolution and a smaller decay rate in the long time.
Entangled systems with large quantum Fisher information (QFI) can be used to outperform the standard quantum limit of the separable systems in quantum metrology. However, the interaction between the system and the environments inevitably leads to decoherence and decrease of the QFI, and it is not clear whether the entanglement systems can be a better resource than separable systems in the realistic physical condition. In this work, we study the steady QFI of two driven and collectively damped qubits with homodyne-mediated feedback. We show that the steady QFI can be significantly enhanced both in the cases of symmetric feedback and nonsymmetric feedback, and the shot-noise limit of separable states can be surpassed in both cases. The QFI can even achieve the Heisenberg limit for appropriate feedback parameters and initial conditions in the case of symmetric feedback. We also show that an initial-condition-independent steady QFI can be obtained by using nonsymmetric feedback.
By using the non-Markovian master equation, we investigate the effect of the cavity and the environment on the quantum Fisher information (QFI) of an atom qubit system in a dissipation cavity. We obtain the formulae of QFI for two different initial states and analyze the effect of the atom–cavity coupling and the cavity–reservoir coupling on the QFI. The results show that the dynamic behavior of the QFI is obviously dependent on the initial atomic states, the atom–cavity coupling, and the cavity–reservoir coupling. The stronger the atom–cavity coupling, the quicker the QFI oscillates, and the slower the QFI decreases. In particular, the QFI will tend to be a stable value rather than zero if the atom–cavity coupling is large enough. On the other hand, the smaller the cavity–reservoir coupling, the stronger the non-Markovian effect, and the slower the QFI decays. In other words, choosing the best parameter can improve the accuracy of the parameter estimation. In addition, the physical explanation of the dynamic behavior of the QFI is given by means of the QFI flow.
Abstract In science and technology, precision measurement of physical quantities is crucial, and the quantum Fisher information (QFI) plays a significant role in the study of quantum systems. In this work, we explore the dynamics of QFI in a hybrid optomechanical system, which consists of a ♢-type four-level atom interacting with a single-mode quantized field via a multi-photon process. We account for various sources of dissipation, including the decay rates of the atom, the cavity and the mechanical modes. Using an effective Hamiltonian, we analytically derive the explicit form of the state vector of the entire system via the time-dependent Schrödinger equation. We then investigate the atomic QFI for the estimation precision of the decay rate of the mechanical oscillator. Furthermore, we examine how optomechanical and atom-field coupling strengths, dissipation parameters and multi-photon transition influence the dynamics of atomic QFI. Our numerical results suggest that the estimation precision of the decay rate of the mechanical oscillator can be controlled by these parameters.
In quantum information technologies, quantum weak measurement is beneficial for protecting coherence of systems. In order to further improve the protection effect of quantum weak measurement on coherence, we propose an optimization scheme of quantum Fisher information (QFI) protection in an open quantum system by combing no-knowledge quantum feedback control with quantum weak measurement. On the basis of solving the dynamic equations of a stochastic two-level quantum system under feedback control, we compare the effects of different feedback Hamiltonians on QFI and find that via no-knowledge quantum feedback, the observation operator σx (or σx and σz ) can protect QFI for a long time. Namely, no-knowledge quantum feedback can improve the estimation precision of feedback coefficient as well as that of detection coefficient.