The nonunital non-Markovian dynamics of qubits immersed in a spin bath is studied without any Markovian approximation. The environmental effects on the precisions of quantum parameter estimation are taken into account. The time-dependent transfer matrix and inhomogeneity vector are obtained for the description of the open dynamical process. The dynamical behaviour of one qubit coupled to a spin bath is geometrically described by the Bloch vector. It is found out that the nonunital non-Markovian effects can engender the improvement of the precision of quantum parameter estimation. This result contributes to the environment-assisted quantum information theory.
The nonunital non-Markovian dynamics of qubits immersed in a spin bath is studied without any Markovian approximation. The environmental effects on the precisions of quantum parameter estimation are taken into account. The time-dependent transfer matrix and inhomogeneity vector are obtained for the description of the open dynamical process. The dynamical behaviour of one qubit coupled to a spin bath is geometrically described by the Bloch vector. It is found out that the nonunital non-Markovian effects can engender the improvement of the precision of quantum parameter estimation. This result contributes to the environment-assisted quantum information theory.
We explore the nonunital non-Markovian dynamics of a qubit immersed in a spin bath. The nonunital environmental effects on the precisions of quantum parameter estimation are investigated. The time-dependent transfer matrix and inhomogeneity vector are obtained for the description of the open dynamical process. The evolution of the coherent vectors for a qubit is studied so as to geometrically demonstrate the nonunital non-Markovian effects. The revivals of angles for the fidelity between a maximal mixed state and an arbitrary trajectory state are presented in the nonunital non-Markovian dynamics. The degree for the nonunitality is controllable with the changes of the local magnetic field for a qubit and spin bath temperature. It is found out that the increase of quantum Fisher information for composite states is connected with the nonunital non-Markovian effects, which is helpful for the improvement of quantum metrology.
The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the 'spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.
The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the `spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.
The quantum Fisher information, the quantum analog of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using numerically exact methods applied to a paradigmatic open quantum system, the spin-boson model, we calculate both static and dynamical quantum Fisher information matrix elements with respect to spin-bath couplings and magnetic field strengths. As the spin-bath interaction increases, we first show that the coupling-coupling matrix elements relative to the ground state of the Hamiltonian are linked to the entanglement growth and signal the Berezinskii-Kosterlitz-Thouless quantum phase transition through their nonmonotonic behavior. We also point out that the static quantum Fisher information exhibits a nonperturbative behavior in the zero-coupling limit, which we justify with an analytic argument. Furthermore, we demonstrate that the time-dependent matrix elements can reveal non-Markovian effects as well as the transition from the coherent to incoherent regime at the Toulouse point, remaining robust under pure dephasing noise. Nonmonotonic signatures of the quantum Fisher information matrix reflect changes in quantum resources such as entanglement and coherence, quantify non-Markovian behavior, and enable criticality-enhanced quantum sensing, thereby shedding light on key features of open quantum systems.
Abstract In the field of quantum information theory, the intersection of the complex dynamics related to non-Markovianity and information is a crucial frontier. Non-Markovian effects, which take memory and temporal correlations into account, challenge conventional wisdom in the fields of quantum biology, metrology, cryptography, and communication. In this work, we analyze the non-Markovian dynamics of a dephasing model in presence of initial system-bath (SB) correlations. These SB correlations are generated via projective measurements on a predefined equilibrium state. Using the non-Markovian measures based on trace distance and quantum Fisher information, it is shown that these correlations have significant impact in the non-Markovian regime at high temperatures while it does not play any role in the Markovian case. Furthermore, it is shown that the oscillatory behaviour of the decoherence function does not always show non-Markovian behaviour.
Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity γ, the squeezed direction θ and squeezed strength r. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller γ or bigger p-quadrature. Interestingly, when 0<θ<π/2, the squeezed quadrature is determined by the combination of r and θ, and by numerical simulation we find that the fidelity peak occurs at r=1−2θ/π. The fidelities increase with increasing r when r∈(0,1−2θ/π]. When θ≥π/2, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.