Einstein-Podolsky-Rosen Steering and Nonlocality in Open Quantum Systems

We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.

Controlling of entropic uncertainty in open quantum system via proper placement of quantum register

We investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty and its lower bound in the amplitude-damping channel. The influences of different placement positions of the quantum register on the dynamics of quantum coherence, quantum entanglement, and quantum discord are analyzed in detail. The numerical simulation results show that the quantum register should be placed in the channel of the non-Markovian effect. This option is beneficial to reduce the entropic uncertainty and its lower bound. We also find that this choice does not change the evolution of the quantum coherence and quantum entanglement, but changes the dynamical process of the quantum discord of the system.These results show that quantum coherence, quantum entanglement, and quantum discord are different quantum resources with unique characteristics and properties, and quantum discord can play a key role in reducing the uncertainty of quantum systems.

Optimal parameter estimation of open quantum systems

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 operatorσx(orσx andσz)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.

Fine-grained uncertainty relation for open quantum system

The fine-grained uncertainty relation (FUR) is investigated for accelerating open quantum system, which manifests the celebrated Unruh effect, a crucial piece of the jigsaw for combining relativity and quantum physics. For a single detector, we show that the inevitable Unruh decoherence can induce a smaller FUR uncertainty bound, which indicates an additional measurement uncertainty may exist. For an open system combined with two detectors, via a nonlocal retrieval game, the related FUR uncertainty bound is determined by the non-classical correlation of the system. By estimating the maximal violation of Bell inequality for an accelerating system, we show that the FUR uncertainty bound can be protected from Unruh decoherence, due to quantum correlation generated through Markovian dynamics.

Robust Set Stabilization and Its Instances for Open Quantum Systems

We propose and discuss a novel concept of robust set stabilization by permissible controls; this concept is helpful when dealing with both a priori information of model parameters and different permissible controls including quantum measurements. Both controllability and stabilization can be regarded as the special case of the novel concept. An instance is presented for a kind of uncertain open quantum systems to further justify this gen- eralized concept. It is underlined that a new type of hybrid control based on periodically perturbed projective measurements can be the permissible control of uncertain open quantum systems when perturbed projective measurements are available. The sufficient conditions are given for the robust set stabilization of uncertain quantum open systems by the hybrid control, and the design of the hybrid control is reduced to selecting the period of measurements.

Influence of homodyne-based feedback control on the entropic uncertainty in open quantum system

For an open quantum system containing two qubits under homodyne-based feedback control, we investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty.Moreover, we analyze the influence of feedback modes and coefficients on the entropic uncertainty.Numerical investigations show that the memory qubit should be placed in a non-dissipative channel if the single dissipative channel condition can be chosen, which helps reduce the entropic uncertainty of the system.For the homodyne feedback control F =λσx(or F =λσy), due to different roles of the entangled qubits A and B, when they are subject to feedback control with different feedback coefficients λ, the exchange of feedback coefficients will cause variations of the entropic uncertainty.When the feedback coefficient corresponding to the memory qubit B is larger(λB >λA), the steady value of the entropic uncertainty will be small, which is conducive to enhancing the robustness of the system.However, for the feedback control F =λσz, the difference between the feedback coefficients has no effect on the steady values of the entropic uncertainty.

Open quantum system approach for heavy quark thermalization

We treat heavy quark as an open quantum system in a hot medium and rederive the stochastic Schrodinger equation(SSE)from the full Schrodinger equation for both heavy quarks and the medium.We apply the SSE to the dynamical evolutions of a heavy quark(as a system)in the static hot medium(as an environment).Heavy quarks interact with the medium via random scatterings,which exchange the momentum and phase factor randomly between two wave functions of the system and the environment.The exchange of momentum and phase factor results in the transition between different eigenstates of the system.These are included via an external stochastic potential in the Hamiltonian of SSE.Stochastic wave functions of a heavy quark are evolved with the stochastic external potential.The mean wave functions and corresponding momentum distributions of heavy quarks are obtained after the ensemble average over a large set of stochastic wave functions.We present the thermalization of heavy quarks in the static medium with different coupling strengths.

Application of non-Hermitian Hamiltonian model in open quantum optical systems

Non-Hermitian systems have observed numerous novel phenomena and might lead to various applications.Unlike standard quantum physics,the conservation of energy guaranteed by the closed system is broken in the non-Hermitian system,and the energy can be exchanged between the system and the environment.Here we present a scheme for simulating the dissipative phase transition with an open quantum optical system.The competition between the coherent interaction and dissipation leads to the second-order phase transition.Furthermore,the quantum correlation in terms of squeezing is studied around the critical point.Our work may provide a new route to explore the non-Hermitian quantum physics with feasible techniques in experiments.

Quantum speed-up capacity in different types of quantum channels for two-qubit open systems

A potential acceleration of a quantum open system is of fundamental interest in quantum computation, quantum communication, and quantum metrology. In this paper, we investigate the ＂quantum speed-up capacity＂ which reveals the potential ability of a quantum system to be accelerated. We explore the evolutions of the speed-up capacity in different quantum channels for two-qubit states. We find that although the dynamics of the capacity is varying in different kinds of channels, it is positive in most situations which are considered in the context except one case in the amplitude-damping channel. We give the reasons for the different features of the dynamics. Anyway, the speed-up capacity can be improved by the memory effect. We find two ways which may be used to control the capacity in an experiment： selecting an appropriate coefficient of an initial state or changing the memory degree of environments.

Quantum Teleportation with an Accelerated Partner in Open System

We investigate the teleportation between two relatively accelerating partners undergoing the phase flip, bit flip and bit-phase flip channels. We find that: 1) the fidelity decreases by increasing the acceleration of accelerated observer;2) the dynamic evolution of the fidelity is different for various channels if the acceleration is fixed;and 3) the fidelity is always symmetric about β2=1/2 where βis a parameter of the transmission state.

Distribution of non-Markovian intervals for open qubit systems

We study the non-Markovianity of open qubit systems using the measure N proposed by Breuer, Laine and Piilo [Phys. Rev. Lett. 103 210401 （2009）]. We find that for the three types of quantum noises, amplitude-damping, dephasing and depolarizing noises, there exist some non-Markovian time intervals whose distribution is independent of the selection of the pair of initial states. Therefore, the maximization in the definition of measure N can be actually removed without influencing the detection of non-Markovianity.

Averaging in SU(2) open quantum random walk

We study the average position and the symmetry of the distribution in the SU（2） open quantum random walk （OQRW）. We show that the average position in the central limit theorem （CLT） is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.

Quantum interferometric power and non-Markovianity in the decoherence channels

In quantum open systems,non-Markovianity is an important phenomenon that allows a backflow of information from the environment to the system.In this work,we investigate the non-Markovianity problems in two different types of channels,where the system-environment interactions are treated with and without the rotating-wave approximation(RWA).We employ the quantum interferometric power(QIP)to quantify the non-Markovian dynamics,which is the minimal quantum Fisher information obtained by the local unitary evolution in a bipartite system.By the hierarchy equation method,we calculate the dynamical evolution of the QIP in the non-RWA case.The results show that the dynamical behavior under the non-RWA is significantly different from that under the RWA in both weak and strong coupling.Moreover,in the non-RWA case,we also find the nonmonotonic behavior of the non-Markovianity measure with the variation of coupling strength,which is caused by the competition between the rotating-wave terms and the counterrotating-wave terms.As a result,we highlight the importance of the counterrotating-wave terms for the influence of non-Markovianity.

Parameter estimation in n-dimensional massless scalar field

Quantum Fisher information(QFI)associated with local metrology has been used to parameter estimation in open quantum systems.In this work,we calculated the QFI for a moving Unruh-DeWitt detector coupled with massless scalar fields in n-dimensional spacetime,and analyzed the behavior of QFI with various parameters,such as the dimension of spacetime,evolution time,and Unruh temperature.We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time.Additionally,we noted that the QFI for small evolution times is several orders of magnitude higher than the QFI for long evolution times.We also found that the value of QFI decreases at first and then stabilizes as the Unruh temperature increases.It was observed that the QFI depends on initial state parameterθ,and Fθis the maximum forθ=0 orθ=π,Fφis the maximum forθ=π/2.We also obtain that the maximum value of QFI for state parameters varies for different spacetime dimensions with the same evolution time.

控制开放超导量子电路系统中的几何量子关联冻结和量子相干性

本文研究了开放超导量子电路系统中,含时电磁场对两超导量子比特间的几何量子关联和量子相干性的影响.我们发现,加入磁场之后,几何量子关联被冻结的现象会出现,并且冻结的时间会随着含时电磁场的加入而得到延长.利用迹距离的方法,我们探讨了含时电磁场对超导量子比特与环境之间量子信息流动的影响,我们发现含时电磁场可以抑制环境的影响,降低超导量子比特与环境之间的量子信息流动.

Quantum speed limit time and entanglement in a non-Markovian evolution of spin qubits of coupled quantum dots

Quantum speed limit time and entanglement in a system composed of coupled quantum dots are investigated.The excess electron spin in each quantum dot constitutes the physical system(qubit).Also the spin interaction is modeled through the Heisenberg model and the spins are imposed by an external magnetic field.Taking into account the spin relaxation as a non-Markovian process,the quantum speed limit and entanglement evolution are discussed.Our findings reveal that increasing the magnetic field leads to the faster quantum evolution.In addition,the temperature increment causes the longer quantum speed limit time as well as the entanglement degradation.

Dynamical learning of non-Markovian quantum dynamics

We study the non-Markovian dynamics of an open quantum system with machine learning.The observable physical quantities and their evolutions are generated by using the neural network.After the pre-training is completed,we fix the weights in the subsequent processes thus do not need the further gradient feedback.We find that the dynamical properties of physical quantities obtained by the dynamical learning are better than those obtained by the learning of Hamiltonian and time evolution operator.The dynamical learning can be applied to other quantum many-body systems,non-equilibrium statistics and random processes.

Influences of spin-orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots

Quantum speed limit and entanglement of a two-spin Heisenberg XYZ system in an inhomogeneous external magnetic field are investigated.The physical system studied is the excess electron spin in two adjacent quantum dots.The influences of magnetic field inhomogeneity as well as spin-orbit coupling are studied.Moreover,the spin interaction with surrounding magnetic environment is investigated as a non-Markovian process.The spin-orbit interaction provides two important features:the formation of entanglement when two qubits are initially in a separated state and the degradation and rebirth of the entanglement.

Quantum Path Predictability for an Electronic Mach-Zehnder Interferometer in Presence of Environment Induced Decoherence and Quantum Erasing Process

In this paper, we have estimated the temperature dependent path predictability for an electronic Mach-Zehnder interferometer. The increment of path predictability can directly be associated with stronger decoherence process. We have also theoretically predicted that placing two detectors in both the paths, which are at the same equilibrium temperature with the system, erases all the memory of path information and hence acts like a quantum eraser.