Dynamical Change of Quantum Fisher Information of Cavity-Reservoir Systems

We study the quantum Fisher information(QFI) dynamics of the phase parameter in the enlarged cavityreservoir systems at zero temperature under two situations of large N limit and non-Markovian environment,respectively.We find an important relation that the total quantities of QFI of the cavity and reservoir are equal to unit during the dynamical evolution.The lost QFI of the cavity transfers to its corresponding reservoir with the same quantities simultaneously.Moreover,we also find that the detuning parameter and non-Markovian effect are two significant factors to affect the preservation of QFI.     

Quantum Fisher information of a qubit-qutrit system in Garfinkle–Horowitz–Strominger dilation space–time

We investigate the quantum Fisher information(QFI) of a qubit-qutrit system in the background of Garfinkle–Horowitz–Strominger dilation black hole. After deriving the analytical expression of the QFI, we examine its dynamics with respect to the dilation parameter D and the state parameter γ of the system. Our results show that the QFI for the estimation of γ is a fixed value,which is independent of the parameters D and γ. And the QFI for the estimation of D varies with the parameters D and γ. Additionally, we propose an effective strategy to steer the QFI by introducing weak measurement reversal. We find that the QFI can be remarkably enhanced by adjusting the appropriate reversing measurement strengths. Our findings might provide some useful insights for the study on parameter estimation of hybrid systems in the framework of relativity theory.     

Quantum Fisher Information for Density Matrices with Arbitrary Ranks

We provide a new expression of the quantum Fisher information （QFI） for a general system. Utilizing this expression, the QFI for a non-full rank density matrix is only determined by its support. This expression can bring convenience for an infinite-dimensional density matrix with a finite support. Besides, a matrix representation of the QFI is also given.     

噪声对一种三粒子量子探针态的影响

量子度量学是研究量子测量与统计推断的一门学科,主要利用量子手段来提高参数估计的精度,在量子信息处理与测量中起到关键作用.量子参数估计的一般过程包含四个步骤:探针态的制备、参数化过程、对参数化后的输出态进行测量以及根据测量结果估计待测参数.其中探针态的选取对测量精度起着至关重要的作用.然而在实际的量子探针态的制备过程中,初始探针态会受到环境噪声的影响.目前人们已经研究了W态与Greenberger-Horne-Zeilinger(GHZ)态的量子Fisher信息(QFI)在典型噪声通道下的变化行为.由于W态与GHZ态有着不同的纠缠性质,对于W态与GHZ态的叠加态的QFI动力学研究具有重要的实际意义.故此,本文主要研究典型噪声通道对这两种状态的叠加态的QFI动力学行为的影响,得出了QFI随噪声参数的变化行为.结果表明,叠加态中W态组分可明显对抗相位阻尼噪声对探针态的QFI的影响,而其中的GHZ态组分可明显对抗振幅阻尼噪声的影响,从而为在实际环境中选取高精度的参数估计过程提供参考.     

Protecting Quantum Fisher Information in Correlated Quantum Channels

Quantum Fisher information (QFI) has potential applications in quantum metrology tasks. QFI is investigated when the consecutive actions of a quantum channel on the sequence of qubits have partial classical correlations. The results showed that while the decoherence effect is detrimental to QFI, effects of such classical correlations on QFI are channel-dependent. For the Bell-type probe states, the classical correlations on consecutive actions of the depolarizing and phase flip channels can be harnessed to improve QFI, while the classical correlations in the bit flip and bit-phase flip channels induce a slight decrease of QFI. For a more general parameterization form of the probe states, the advantage of using the initial correlated system on improving QFI can also remain in a wide regime of the correlated quantum channels.     

Enhancing the Precision of Parameter Estimation in Band Gap

Recently, the dynamics of quantum Fisher information(QFI) in various environment are investigated and many kinds of schemes to overcome the drawback of decoherence are designed. Here we propose the pseudomode method to enhance the phase parameter precision of optimal quantum estimation of a qubit coupled to a non-Markovian structured environment. We find that the QFI can be enhanced in the weak-coupling regime with non-perfect band gap and can be trapped permanently with a large value in the perfect band gap. The effects of qubit-pseudomode detuning and the spectrum of reservoir are discussed, a reasonable physical explanation is given, too.     

The Precision of Parameter Estimation for Dephasing Model Under Squeezed Reservoir

We study the precision of parameter estimation for dephasing model under squeezed environment. We analytically calculate the dephasing factor γ(t) and obtain the analytic quantum Fisher information (QFI) for the amplitude parameter α and the phase parameter ?. It is shown that the QFI for the amplitude parameter α is invariant in the whole process, while the QFI for the phase parameter ? strongly depends on the reservoir squeezing. It is shown that the QFI can be enhanced for appropriate squeeze parameters r and θ. Finally, we also investigate the effects of temperature on the QFI.     

基于部分测量增强量子隐形传态过程的量子Fisher信息

量子Fisher信息(QFI)是量子度量学中的一个重要物理量,可给出预估参数精度的最优值.本文研究如何引入弱测量和测量反转操作,来提高有限温环境下以Greenberger-Horne-Zeilinger态作为量子通道的隐形传态过程中的QFI.依据隐形传态过程中量子比特的传输情形,考虑了三种不同方案相应的QFI.首先,通过构造每种量子隐形传态方案的量子线路图,分析了QFI与推广振幅衰减噪声参数的变化关系.随后对各种方案中的受噪声粒子施加弱测量和测量反转操作,并对相应的部分测量参数进行优化,着重探讨了施加最优部分测量操作后QFI的改进量.结果表明,经过优化后的部分测量操作能有效提高有限温环境下量子隐形传态过程输出态的QFI;而且量子系统所处的环境温度越低,QFI的提高效果可越显著.     

Quantum metrology with a non-Markovian qubit system

The dynamics of the quantum Fisher information(QFI) of phase parameter estimation in a non-Markovian dissipative qubit system is investigated within the structure of single and double Lorentzian spectra. We use the time-convolutionless method with fourth-order perturbation expansion to obtain the general forms of QFI for the qubit system in terms of a non-Markovian master equation. We find that the phase parameter estimation can be enhanced in our model within both single and double Lorentzian spectra. What is more, the detuning and spectral width are two significant factors affecting the enhancement of parameter-estimation precision.     

Quantum Fisher information width in quantum metrology

In scenarios of quantum metrology, the unitary parametrization process often depends on space directions. How to characterize the sensitivity of parameter estimation to space directions is a natural question. We propose the concept of the quantum Fisher information(QFI) width, which is the difference between the maximum and minimum values of the QFI, to quantitatively study the sensitivity. We find that Fock states, the bosonic coherent states, and the displaced Fock states all have zero widths, indicating that QFI is completely inert over all directions, while the width for the spin state with all spins down or up is equal to the number of particles, so this concept will enable us to choose appropriate directions to make unitary transformation to obtain larger QFI.The QFI width of the displaced quantum states is found to be independent of the magnitude of the displacement for both spin and bosonic systems. We also find some relations between the QFI width and squeezing parameters.     

Transmission of Quantum Fisher Information through Fluctuating Quantum Fields

Transmission of quantum Fisher information (QFI) of initially disentangled parties is studied and the results show that the indirect correlations generated by the environment, which is considered as a bath of fluctuating quantum fields, will help transmit the quantum information. Specifically, using N initially disentangled atoms—one in an excited state carried by one party (the sender, Alice) and the other in the ground state carried by the other parties (the receivers: Bob1, Bob2,…, Bob(N?1)), the phase factor of the state of another atom held by Alice can be transmitted from Alice to Bob with proper time. The transmitted QFI of the phase factor for each receiver has been calculated as a function of the transmitted distance as well as the measurement time and is found to be in relation with the concurrence of the pair of atoms that the sender and the receiver carry. For each transmitted distance, there exists an optimal measurement time to obtain the maximal transmitted QFI, which is in relation with the total number of receivers.     

Improving the teleportation of quantum Fisher information under non-Markovian environment

Quantum teleportation is designed to send an unknown quantum state between two parties. In the perspective of remote quantum metrology, one may be interested in teleporting the information that is encoded by physical parameters synthesized by quantum Fisher information (QFI). However, the teleported QFI is often destroyed by the unavoidable interaction between the system and the environment. Here, we propose two schemes to improve the teleportation of QFI in the non-Markovian environment. One is to control the quantum system through the operations of weak measurement (WM) and corresponding quantum measurement reversal (QMR). The other is to modify the quantum system based on the monitoring result of the environment (i.e., environment-assisted measurement, EAM). It is found that, in the non-Markovian environment, these two schemes can improve the teleportation of QFI. By selecting the appropriate strengths of WM and QMR, the environment noise can be completely eliminated and the initial QFI is perfectly teleported. A comprehensive comparison shows that the second scheme not only has a higher probability of success than the first one, but also has a significant improvement of the teleported QFI.     

Dynamics of quantum Fisher information in a two-level system coupled to multiple bosonic reservoirs

We consider the optimal parameter estimation for a two-level system coupled to multiple bosonic reservoirs. By using quantum Fisher information(QFI), we investigate the effect of the Markovian reservoirs' number N on QFI in both weak and strong coupling regimes for a two-level system surrounded by N zero-temperature reservoirs of field modes initially in the vacua. The results show that the dynamics of QFI non-monotonically decays to zero with revival oscillations at some time in the weak coupling regime depending on the reservoirs' parameters. Furthermore, we also present the relations between the QFI flow, the flows of energy and information, and the sign of the decay rate to gain insight into the physical processes characterizing the dynamics.     

Enhancement of Sensitivity by Initial Phase Matching in SU(1,1) Interferometers

We derive a general phase-matching condition(PMC) for enhancement of sensitivity in SU(1,1) interferometers. Under this condition, the quantum Fisher information(QFI) of two-mode SU(1,1) interferometry becomes maximal with respect to the relative phase of two modes, for the case of an arbitrary state in one input port and an even(odd) state in the other port, and the phase sensitivity is enhanced. We also find that optimal parameters can let the QFI in some areas achieve the Heisenberg limit for both pure and mixed initial states. As examples, we consider several input states: coherent and even coherent states, squeezed vacuum and even coherent states, squeezed thermal and even coherent states. Furthermore, in the realistic scenario of the photon loss channel, we investigate the effect of photon losses on QFI with numerical studies. We find the PMC remains unchanged and is not affected by the transmission coefficients for the above input states. Our results suggest that the PMC can exist in various kinds of interferometers and the phase-matching is robust to even strong photon losses.     

Improving Quantum Metrology via Purifying and Distilling Noisy Probe States

In quantum metrology, the precision of unknown parameter estimation is studied in the quantum regime, and the choice of the probe state plays an important role in determining the precision of the parameter to be estimated. The quality of quantum metrology will be reduced in the presence of quantum noise during the memory time of probe states after preparation. Meanwhile the noisy probe state can be manipulated by different protocols such as single‐qubit purification, entanglement purification, and entanglement distillation etc. In this paper, the effects of these manipulations on the usefulness, that is, quantum Fisher information (QFI), of the noisy probe state in quantum metrology are studied. The results show that joint operations in single‐qubit purification and entanglement purification processes play positive roles in enhancing the QFI of the probe states, and local measurements in entanglement purification and entanglement distillation processes play both positive and negative roles in enhancing the QFI of the probe states. In this sense, single‐qubit purification will always be helpful in parameter estimation by using single qubits as probe, and entanglement purification process maybe more suitable for improving the estimation precision when entangled‐state probe is adopted.     

Dynamics of a Moving Two-Level Atom Under the Influence of Intrinsic Decoherence

We present a general and fascinating problem of quantum entanglement (QE) that is calculated with the help of quantum Fisher information (QFI) and von Neumann entropy (VNE) for moving two-level atomic systems. We calculate numerically the temporal evolution of the state vector of the entire system under the influence of intrinsic decoherence for a moving two-level atom. We demonstrate that the phase shifts of an estimator parameter, intrinsic decoherence, and the atomic motion play an important and prominent role during the time evolution of the atomic system. We observe that there is a monotonic relation between the atomic quantum Fisher information (QFI) and quantum entanglement (QE) in the absence of atomic motion. We also show that at the revival time the local maximum values of QFI decreases gradually. A periodic behavior of QFI is observed in the presence of atomic motion, which becomes more important and remarkable for two-level atomic systems. Moreover, the atomic quantum Fisher information and entanglement demonstrate an opposite response during the time evolution in the presence of atomic motion. We show that the evolution of entanglement is more susceptible to the intrinsic decoherence; a considerable change occurs in the degree of entanglement when the intrinsic decoherence parameter increases. Intrinsic decoherence in the atom–field interaction represses the nonclassical effects of the atomic systems. Both the entanglement and the quantum Fisher information saturate to their lower levels for longer time scales in the presence of intrinsic decoherence. For larger values of intrinsic decoherence, the sudden death of entanglement is observed.     

Dynamics of Quantum Fisher Information in Homodyne-Mediated Feedback Control

We investigate the quantum Fisher information(QFI) dynamics of a dissipative two-level system in homodynemediated 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.     

Phase estimation of phase shifts in two arms for an SU(1,1) interferometer with coherent and squeezed vacuum states

We theoretically study the quantum Fisher information(QFI) of the SU(1,1) interferometer with phase shifts in two arms by coherent ? squeezed vacuum state input, and give the comparison with the result of phase shift only in one arm.Different from the traditional Mach–Zehnder interferometer, the QFI of single-arm case for an SU(1,1) interferometer can be slightly higher or lower than that of two-arm case, which depends on the intensities of the two arms of the interferometer.For coherent ? squeezed vacuum state input with a fixed mean photon number, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.     

Time-local optimal control for parameter estimation in the Gaussian regime

Information about a classical parameter encoded in a quantum state can only decrease if the state undergoes a non-unitary evolution, arising from the interaction with an environment. However, instantaneous control unitaries may be used to mitigate the decrease of information caused by an open dynamics. A possible, locally optimal (in time) choice for such controls is the one that maximises the time-derivative of the quantum Fisher information (QFI) associated with a parameter encoded in an initial state. In this study, we focus on a single bosonic mode subject to a Markovian, thermal master equation, and determine analytically the optimal time-local control of the QFI for its initial squeezing angle (optical phase) and strength. We show that a single initial control operation is already optimal for such cases and quantitatively investigate situations where the optimal control is applied after the open dynamical evolution has begun.     

Quantum Fisher Information of Several Qubitsin the Superposition of A GHZ and two W Stateswith Arbitrary Relative Phase

We study the quantum Fisher information (QFI) of a system of several particles which is in a superposition of a GHZ and two W states with arbitrary relative phase. We show that as the number of particles increases from 3 to 4, the behavior of QFI drastically changes. We also show how the dependence of QFI on the relative phase weakens as the number of particles increases. We also analyze the QFI for the state for several instances of N due to the change of the relative phases.