In this work, we investigate the non-Markovianity, quantum Fisher information (QFI) and quantum coherence of a qubit in a nonequilibrium environment and have obtained the expressions of QFI and quantum coherence as well as their relationship. We have also discussed in detail the influences of the different noise parameters on these quantum sffects. The results show that the suitable parameters of the nonequilibrium environment can retard the QFI and quantum coherence in both Markovian and non-Markovian regions. In addition, the smaller memory effects and the larger the jumping rate, the greater the QFI and quantum coherence. And a larger QFI naturally corresponds to a larger quantum coherence, which indicates that the quantum coherence can enlarge the QFI and can effectively enhance the quantum metrology.
One of the fundamental issues in the field of open quantum systems is the classification and quantification of non-Markovianity. In the contest of quantity-based measures of non-Markovianity, the intuition of non-Markovianity in terms of information backflow is widely discussed. However, it is not easy to characterize the information flux for a given system state and show its connection to non-Markovianity. Here, by using the concepts from thermodynamics and information theory, we discuss a potential definition of information flux of an open quantum system, valid for static environments. We pr…
By using the quantum Fisher information (QFI), we address the process of \textit{single}-parameter estimation in the presence of bosonic as well as fermionic environments and protection of information against the noise. In particular, the quantum interferometric power (IP) of the evolved state of the system is uncovered as an important lower bound for the QFIs of initially encoded parameters. Moreover, we unveil new witnesses of non-Markovianity, that can be used to detect efficiently the memory effects and backflow of information from the environment to the system. On the other hand, we also …
By using the quantum Yang-Baxterization approach to the three different Hamiltonians, we investigate the behavior of the quantum Fisher information (QFI) under the actions of these Hamiltonians on the different two-qubit input states and by estimating the meaningful parameter $φ$. We address the overall estimation properties by evaluating the QFI for the whole system undergone different unitary evolution. The results show that the behavior of the QFI depends on the choice of the initial states. Choosing the optimal input states can improve the precision of quantum parameter estimation. On the …
We propose to use the quantum Fisher information in characterizing the information flow of open quantum systems. This information-theoretic approach provides a quantitative measure to statistically distinguish Markovian and non-Markovian processes. A basic relation between the QFI flow and non-Markovianity is unveiled for quantum dynamics of open systems. For a class of time-local master equations, the exactly-analytic solution shows that the non-Markovianity is characterized by additive information sub-flows in different non-Markovian channels.
Closed quantum systems obey the Schroedinger equation whereas nonequilibrium behavior of many of systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between those two types of behavior. We discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes. This is first principally addressed based on the notions of "consistency" and "Markovianity." Numerical data are presented that show that the above conditions are to good approximation fulfilled for Heisenberg-type …
In this study, we apply quantum master equations beyond secular approximation, and investigate the nonequilibrium thermodynamic cost of enhanced quantum metrology and quantum correlations. We find that the nonequilibrium conditions enhance quantum Fisher information (QFI) and quantum correlations predominantly for weak tunneling scenarios. The enhancement is assisted by a corresponding increase of the thermodynamic cost characterized by the entropy production rate (EPR). For the strong tunneling regimes, the QFI and quantum correlations can not be unceasingly boosted by higher thermodynamic co…
We explore signatures of the non-Markovianity in the time-resolved energy transfer processes for quantum open systems. Focusing on typical systems such as the exact solvable damped Jaynes-Cummings model and the general spin-boson model, we establish quantitative links between the time-resolved energy current and the symmetric logarithmic derivative quantum Fisher information (SLD-QFI) flow, one of measures quantifying the non-Markovianity, within the framework of non-Markovian master equations in time-local forms. From the relationships, we find in the damped Jaynes-Cummings model that the SLD…
Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond en…
We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open system states, and on a principle of minimal dissipation. This principle leads to a unique prescription for the decomposition of the master equation into a Hamiltonian part representing coherent time evolution and a dissipator part describing dissipation and decoherence. Employing this decomposition we demonstrate how to define work, heat, and entropy production…
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér-Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the pr…
Understanding heat transfer between a quantum system and its environment is of undisputed importance if reliable quantum devices are to be constructed. Here, we investigate the heat transfer between system and bath in non-Markovian open systems in the process of adiabatic speedup. Using the quantum state diffusion equation method, the heat current, energy current, and power are calculated during free evolution and under external control of the system. While the heat current increases with increasing system-bath coupling strength and bath temperature, it can be restricted by the non-Markovian n…
Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovian dynamics. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovian dynamics and when it does not. This is established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a system in cont…
In a fully-controllable experiment platform for studying non-Markovian open quantum dynamics, we show that the non-Markovianity could be investigated from the global and local aspects. By mixing random unitary dynamics, we demonstrate non-Markovian and Markovian open quantum dynamics. From the global point of view, by tuning the base frequency we demonstrate the transition from the Markovianity to the non-Markovianity as measured by the quantum mutual information (QMI). In a Markovian open quantum process, the QMI decays monotonically, while it may rise temporarily in a non-Markovian process. …
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lead to classical Fisher information. In this article, we exploit the classical Fisher information induced by quantum measurements, and reveal a rich hierarchical structure of such measurement-induced Fisher information. We establish a general framework for the distribution and transfer of the Fisher information. In particular, we illustrate three ext…
We consider two non-Markovian models: Random Telegraph Noise (RTN) and non-Markovian dephasing (NMD). The memory in these models is studied from the perspective of quantum Fisher information flow. This is found to be consistent with the other well known witnesses of non-Markovianity. The two noise channels are characterized quantum information theoretically by studying their gate and channel fidelities. Further, the quantum coherence and its balance with mixedness is studied. This helps to put in perspective the role that the two noise channels can play in various facets of quantum information…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the related Fisher information notion, which jointly account for the shape and extension of continuous probability distributions. Classical, dynamical and random systems in general give rise to time-dependent probability densities and associated information measures. The induced dynamics of Shannon and Fisher functionals reveals an interplay among various charac…
We consider the dynamics of maximal quantum Fisher information (MQFI) after sudden quenches for the one-dimensional transverse-field Ising model. Our results show, the same as Loschmidt echo, there is a universality for the revival times i.e., they do not depend on the initial state and the size of the quench and are given by integer multiples of $T_{rev} \simeq \frac{N}{2v_{max }}$, where $N$ is the system size and $v_{max }$ is the maximal group velocity of quasiparticles. Critically enhanced and decreased at revival and decay times as $T_{rev} \equiv T_{dec} $ are characterized by quenching…
The problem of quantum metrology under the context of a particular non-Markovian quantum evolution is explored. We study the dynamics of the quantum Fisher information (QFI) of a composite quantum probe coupled to a Lorentzian environment, for a full variety of different classes of parameters. We are able to find the best metrological state which is not maximally entangled but is the one which evolves fastest. This is shown by evidencing a connection between QFI and different quantum speed limits. At the same time, by optimizing a control field acting over the probes, we show how the total inf…
Any realistic quantum system is inevitably subject to an external environment. This environment makes the open-system dynamics significant for many quantum tech-nologies, such as entangled-state engineering, quantum simulation, and quantum sensing. The information flow of a system to its environment usually induces a Markovian process, while the backflow of information from the environment exhibits non-Markovianity. The practical environment, usually consisting of a large number of degrees of freedom, is hard to control, despite some attempts on controllable transitions from Markovian to non-M…
Nonequilibrium thermometry via an ensemble of initially correlated qubits
Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；Department of Physics and Astronomy, Università di Firenze（佛罗伦萨大学物理与天文学系）；European Laboratory for Non-linear Spectroscopy, Università di Firenze（佛罗伦萨大学欧洲非线性光谱学实验室）
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational principle for its nonequilibrium steady state. We successfully apply our variational method to study dissipative Rydberg gases, finding excellent quantitative agreement with small-scale simulations of the full quantum master equation. We observe that correlations related to non-Markovian behavior play a significant role during the relaxation dynamics toward…
Quantum Fisher information (QFI) is an important feature for the precision of quantum parameter estimation based on the quantum Cramér-Rao inequality. When the quantum state satisfies the von Neumann-Landau equation, the local quantum uncertainty (LQU), as a kind of quantum correlation, present in a bipartite mixed state guarantees a lower bound on QFI in the optimal phase estimation protocol [Phys. Rev. Lett. 110 (2013) 240402]. However, in the open quantum systems, there is not an explicit relation between LQU and QFI generally. In this paper, we study the relation between LQU and QFI in ope…
Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics. However, exact analytical results remain scarce, especially for systems out of equilibrium. In this work we examine a paradigmatic one-dimensional fermionic system that consists of a uniform tight-binding chain with an arbitrary scattering region near its center, which is subject to a DC bias voltage at zero temperature. The system is thus held in a current-carryi…
