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In this paper, we focus on studying how to enhance the precision of parameter estimation by dynamical decoupling (DD) pulses in an open system. Our results show that, when a qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir, the quantum Fisher information (QFI) is determined by the decoherence function of this qubit. If the appropriate DD pulse frequency is selected, the decoherence in noisy environment can be effectively suppressed and the precision in parameter estimation can be enhanced. Moreover, we make a further comparison for the control effects between Uhrig dynamical decoupling (UDD) sequence and periodic dynamic decoupling (PDD) sequence in the sub-Ohmic and super-Ohmic environments. We find that, when the same DD pulses are applied to this qubit, UDD has obvious advantages over PDD in terms of improving precision of parameter estimation. This is because UDD can completely eliminate the adverse effect of environmental decoherence on parameter estimation.

We investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty under the quantum-jump-based feedback control in open systems containing two qubits, and analyze the influence of feedback modes and coefficients on the entropic uncertainty. Numerical investigations indicate that: under quantum-jump-based feedback control, no matter whether qubits A and B are both or alone suffering from the environmental decoherence, when the feedback coefficient is the integer multiples of π/2, the entropic uncertainty of the system is a minimum value, which is far less than that without feedback control. As the dissipative coefficient γ decreases, namely the environmental decoherence decreases, the entropic uncertainty can be greatly improved under the quantum-jump-based feedback control.

We investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under two typical categories of noise: phase damping channel and amplitude damping channel. It is shown that, the entropic uncertainty monotonically increases and tends to a steady-state value with the increase of decoherence in phase damping channel, and can always keep its lower bound during the evolution when the initial state is the maximum entangled state. In contrast, under the amplitude damping channel with memory, the entropic uncertainty always fails to reach its lower bound, even in the decoherence-free subspace formed by it. Besides, the entropic uncertainty and its lower bound firstly increase with time, then turn down and tend to steady-state values. Our investigations might offer an insight into the dynamics of the measurement uncertainty under decoherence, and are important to quantum precision measurement in open systems.

We investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under two typical categories of noise: phase damping channel and depolarizing channel in detail. It shows that, owing to the dissipation, the entropic uncertainty monotonically increases and tends to a steady-state value with the increase of the decoherence in phase damping channel, and can always keep its lower bound during the evolution when the initial state is the maximum entangled state. The larger correlated dephasing rate is favorable for suppressing the amount of entropic uncertainty. In contrast, under the depolarizing channel with memory, the entropic uncertainty always fails to reach its lower bound. Besides, the entropic uncertainty and its lower bound firstly increase with time, then turn down and tend to a steady-state value. The larger correlated decay rate has no benefit to improve the accuracy of quantum measurement. Our investigations might offer an insight into the dynamics of the measurement uncertainty under decoherence, and be important to quantum precision measurement in open systems.

For a high dimensional spin-S system embedded in a dephasing environment, we theoretically analyze the time evolutions of quantum correlation and entanglement via Frobenius norm and negativity. The quantum correlation dynamics can be considered as a function of the decoherence parameters, including the ratio between the system oscillator frequency ω 0 and the reservoir cutoff frequency ω c , and the different environment temperature. It is shown that the quantum correlation can not only measure nonclassical correlation of the considered system, but also perform a better robustness against the dissipation. In addition, the decoherence presents the non-Markovian features and the quantum correlation freeze phenomenon. The former is much weaker than that in the sub-Ohmic or Ohmic thermal reservoir environment.

Fast state transfer of quantum system is one of the effective robust control problems that often appear in practice, which is good for efficiency improving and decoherence suppression caused by the environment. In this paper, we mainly discuss the fast transfer of quantum state in a two-qubit system. By analyzing the advantages and disadvantages of the existing Lyapunov control, we propose that the quantum state transfer can be accelerated by minimizing the Lyapunov function, and give three optimized control field design methods. For the problem of a two-qubit open quantum system, numerical simulation results indicate the effectiveness of the method. Not only the state transfer time is shortened, but also the high-frequency oscillation that occurs in bang–bang control is effectively avoided.

Fast control of the state of quantum system is one of the robust control problems that often appear in practice, which is effective for decoherence suppression caused by the environment. In this paper, on the basis of an analysis of the advantages and disadvantages of the existing Lyapunov control, we propose three improved bang-bang control designs that are composed of the theory of bang-bang control and parameters optimization method and can solve fast control of the state transfer problem for quantum systems. Numerical simulation shows the effectiveness of the method for the problem of a closed two-level quantum system. Not only the decrease of Lyapunov function is fastened, the optimization of control time is realized and the coherence is protected, but also the high-frequency oscillation that occurs in bang-bang control is effectively avoided.

The optimization of control time for quantum systems has been an important field of control science attracting decades of focus, which is beneficial for efficiency improvement and decoherence suppression caused by the environment. Based on analyzing the advantages and disadvantages of the existing Lyapunov control, using a bang-bang optimal control technique, we investigate the fast state control in a closed two-qubit quantum system, and give three optimized control field design methods. Numerical simulation experiments indicate the effectiveness of the methods. Compared to the standard Lyapunov control or standard bang-bang control method, the optimized control field design methods effectively shorten the state control time and avoid high-frequency oscillation that occurs in bang-bang control.

There has long been interest to control the transfer of population between specified quantum states and protect the coherence of the system at the same time. In this paper, from the perspective of engineering implementation, and based on the idea of reverse engineering, we propose a control scheme for state transfer of two-level open quantum system, which is to drive system from arbitrary initial state to desired target state. In order to ensure that the system can process information effectively, we design the control pulse in advance in terms of population number and coherence, and then verify the validity through numerical simulation. The results show that the system can be driven from any initial state to the desired target state by the designed control pulse, and the coherence of the system is well protected during the state transfer. The influences of environmental decoherence on population transfer and coherence control is further discussed. It reveals that the control pulse presented in this paper is robust to the variation of related parameters.

In quantum information processing, rapid control is a basic requirement for performance improvement because a realistic quantum system cannot be perfectly separated from its environment, which will cause relaxation or decoherence effect. Rapid control may make the control law more robust to uncertainties in the model or in the control process. From the time optimization standpoint, bang-bang control is an excellent method for engineering practice. However, quantum bang-bang control relies on quantum Zeno effect, quantum anti-Zeno effect will occur under low measurement frequency, which intensifies the decoherence and leads to high-frequency oscillation phenomenon. In order to realize rapid state transfer and avoid high-frequency oscillation with an infinitesimal period in bang-bang Lyapunov control, we design control fields to realize arbitrary state transfer for non-Markovian system with phase relaxation and energy dissipative relaxation by Lyapunov stability theory. The numerical simulations illustrate that arbitrary state (eigenstate, superposition state or mixed state) transfer and maintenance for non-Markovian system can be realized under the approximate bang-bang Lyapunov control.

In quantum state transfer and tracking, fast control of quantum states are effective against the decoherence caused by external environment and information processing. The variational method and maximum principle are often used to solve the time-optimal control problems. However, analytic results cannot be obtained for many cases and it is necessary to find methods that can solve optimal control problems very efficiently. By comparing the advantages and disadvantages of the existing Lyapunov control and bang–bang control, we apply in this paper a new method that combines bang–bang control and Lyapunov control and can solve the time-optimal control problems in the open quantum system. Numerical simulations for a two-level open quantum system validate the effectiveness of the method. Furthermore, the optimized scheme avoids high frequency oscillation that occurs in bang–bang control.

We study the absorption and dispersion properties of the three levels A-type superconducting quantum circuit driven by a pump field and a relatively weak probe field being applied to the different transitions. We find that the decoherence time between levels is critical to the observation of electromagnetically induced transparency (EIT) in superconducting quantum circuit. When the total decoherence time is fixed, it is necessary to ensure better coherence between levels |3⟩ ↔ |2⟩ than |3⟩ ↔ |1⟩ so as to exhibit obvious EIT. Furthermore, under given probe field, the bigger the Rabi frequency of probe field is, the wider the window of EIT, the easier to observe the transparency window. At this moment, however, slow light is inconspicuous and not conductive to optical information memory.

Decoherence is the main obstacle to quantum precision measurement. One must adopt appropriate control strategies to suppress decoherence. In this paper, we study the dephasing model of the system-environment with initial correlation, and use the quantum Fisher information (QFI) as the tool to explore the effect of dynamical decoupling pulses on inhibiting decoherence and improving the estimation precision of quantum parameters. We firstly study the influence of the initial correlations and initial quantum state on the dynamical evolution of a single qubit in this mode. Based on numerical calculations, in the Ohmic and the super-Ohmic thermal reservoir, we find that the periodic dynamical decoupling (PDD) sequence can significantly reduce the amplitude of the decoherence function, except for the "anti-Zeno" effect when the number of pulses is relatively small. By a judicious choice of the PDD pulse frequency, the dynamical decoupling pulses can effectively enhance the precision of quantum parameter estimation. And due to the peak structure existing in the decoherence function, the effect of applying Uhrig dynamical decoupling (UDD) sequence on the model is not ideal.

Dynamical decoupling (DD) technique is one of the most successful methods to suppress decoherence in qubit systems. In this paper, we studied a solvable pure dephasing model and investigated how DD sequences and initial correlations affect this system. We gave the analytical expressions of decoherence functions and compared the decoherence suppression effects of DD pulses in Ohmic, sub-Ohmic and super-Ohmic environments. Our results show that (1) The initial system-environment correlation will cause additional decoherence. In order to control the dynamic process of open quantum system more accurately and effectively, the initial correlation between the system and reservoir must be considered. (2) High frequency DD pulses can significantly reduce the amplitude of the decoherence function even in the presence of initial system-environment correlations.

The artificial intervention of quantum environment is a basic task of quantum information engineering. In this paper, we investigate the dynamical behaviors of a single system coupled to a spin environment by a z–x-type interaction. We focus on studying how to enhance the precision of parameter by the pre-designed factors of the environment. The numerical simulation results show that the initial state of the environment obviously affects the dynamics of coherence of the central spin system. We find that the environment should be prepared in a block entangled state with Bell state. This option is beneficial to increasing the quantum Fisher information. Further, if the environment is dominated by higher-frequencies particles, the decoherence in noisy environment can be effectively suppressed and the precision of parameter estimation can be enhanced.

The optimal control function for an open system is designed by taking the expectation value of the state under control reaching the target state as the performance indicator. Utilizing Runge Kutta method, the open quantum system with a superconducting qubit is numerically investigated. The influences of parameters on the population transfer probability and control time are compared. The simulation experiments indicate that the state transfer and state maintenance is realized with a success rate of more than 98 percent, which validating the application of optimal control method in the state transfer and maintenance for open quantum system containing superconducting qubits. Moreover, proper increase of the proportional coefficients can accelerate the qubits flip and reduce the vibration frequency of control function.

We study the quantum correlation and entanglement for a high-dimensional spin-S system in a squeezed vacuum reservoir. The exact analytical solution is presented, which shows that the decoherence function governs the quantum correlation and quantum entanglement of corresponding dynamical process. The squeezed amplitude parameter for quantum correlation and quantum entanglement has a negative impact in the whole process, the better the squeezing effect, the greater the negative impact. Furthermore, in the super-Ohmic reservoir, the influence of Ohmic parameter on quantum correlation and quantum entanglement can be divided into two regions in terms of the critical value s = 2.5 ⁡ . If s 2.5 , the decay rate of quantum correlation slows down obviously, and the environmental decoherence effect is much smaller than that of Ohmic and sub-Ohmic reservoirs. On the contrary, if s > 2.5 , the decay rate of quantum correlation accelerates obviously, and the decoherence effect surpasses the cases of Ohmic and sub-Ohmic reservoirs greatly.

In quantum state transfer and tracking, control of quantum states are effective against decoherence caused by external environment and information processing. In this paper, utilizing model reference adaptive control theory and Lyapunov stability theorem, we derive the adaptive law for the model reference adaptive system. Then we design the Lyapunov control law by double control functions and we investigate the orbit tracking of quantum state for Markovian quantum system. Meanwhile, through counteracting the shift term by simplization, the control law avoids oscillating state trajectory in a two-level Markovian quantum system. Finally, numerical simulations for a two-level open quantum system validate the effectiveness of the method.

Quantum robust control has been recognized as a critical issue in quantum systems, since many quantum systems are unavoidably subject to disturbances and uncertainties in practical applications. Considered uncertainty of Hamiltonian in the Markovian quantum system, on one hand this paper define the control effect based on fidelity, purity and degree of coherence, on the other hand design control scheme and acquire the corresponding analytical expression of sampling period based on data sampling. Meanwhile the author discuss about selection of sampling operator and quantum state driven in the process of quantum sampling.

Utilizing the concurrence and the quantum discord as the measure method, in this paper we compare and investigate the dynamic evolution features of quantum correlations of coupled qubits in non-Markovian process. We focus attention on decoherence effect influences the stability of quantum correlations. The investigation results show that because of the decoherence influence between the system and environment, the concurrence always evolves with time in oscillation form in the way of deaths and survivals, however, the quantum discord time evolution does not appear the deaths and survivals. The quantum discord survives obviously longer than concurrence, which indicates that quantum discord has a stronger ability to resist decoherence than entanglement. Through regulating and controlling the purity and entanglement of the initial quantum state, we can effectively suppress the decay of the quantum correlations, which is advantaged to complete the quantum information processing.

In two-level approximation, we studied the influence of the mutual inductive coupling in the superconducting quantum circuits on the decoherence of the flux qubits under super-Ohm thermal reservoir environment by utilizing Bloch–Redfield function. The results show: (1) the memory effect existing in the solid-state environment and the Ohmic thermal reservoir caused by the deformation potential will help to prolong the decoherence time of the superconducting flux qubit, building super-Ohm thermal reservoir environments will be the best candidate available for improving the decoherence of the solid-state qubit. (2) When the quantum system and the thermal reservoir environment are in weak coupling, generally speaking, the mutual coupling effect between circuit elements will destroy the quantum coherence; but when the quantum system and the thermal reservoir environment are in strong coupling, it will be beneficial to enhance the decoherence time by controlling the mutual inductive coupling between the loop components.

The sudden death of entanglement is investigated for non-Markovian dynamic process of a pair interacting flux qubits under a thermal bath. The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that, for initially two-qubit entangled states, the sudden death of entanglement (ESD) always happens in the thermal reservoir, where the appearance of entanglement sudden death strongly depends on the environment. Especially, ESD of the qubits is easier to occur for non-Markovian process than for Markovian one.

The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that the entanglement of quantum systems depends on not only the initial state of system but also the coupling ways between qubit and environment. It shows that: (1) when the system is initially in \(( | 00 \rangle\pm| 11 \rangle)/\sqrt{2}\) state or in the mixed state which is produced by the state, if we can control the coupling between the qubits and the environment in a asymmetrical state, we can make the quantum system always in the entangled state. (2) For an initial state \(( | 01 \rangle\pm| 10 \rangle)/\sqrt{2}\) or in its mixed state, in contrast, there will not be entangled death under the symmetric coupling. We also find that, in \(( | 01 \rangle\pm| 10\rangle)/\sqrt{2}\) or in its mixed state, the stronger the interaction between qubits is, the better to struggle against entanglement sudden death is.

Dynamic evolution of entanglement is studied for coupling two-qubit system in non-Markov environment in terms of concurrence. We find that the degree of entanglement depends on the initial quantum state of the system and the interaction between the two-qubit system and the environment. When the interaction between the qubits and the environment is completely symmetric, especially, the environment has no effect on the entanglement, where the decoherence is entirely resulted from the interaction between qubits. By controlling the coupling way of the interaction, thus, one may avoid the entanglement sudden death (ESD).

A scheme is proposed to controll decoherence of three-level floating qubit by designing an external electric circuit with superconductive flux qubit. The results show that it may not only raise gate speed but also extend decoherence time for three-level structure.

Due to the influence of decoherence, the quantum state probably evolves from the initial pure state to the mixed state, resulting in loss of fidelity, coherence and purity, which is deteriorating for quantum information transmission. Thus, in quantum engineering, quantum control should not only realize the transfer and track of quantum states through manipulation of the external electromagnetic field but also enhance the robustness against decoherence. In this paper, we aim to design a control law to steer the system into the sliding mode domain and maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We first define the required control performance by fidelity, degree of coherence and purity in terms of the uncertainty of the Hamiltonian in Markovian open quantum system. By characterizing the required robustness using a sliding mode domain, a sampled-data design method is introduced for decoherence control in the quantum system. Furthermore, utilizing the sampled data, a control scheme has been designed on the basis of sliding mode control, and the choice of sampling operator and driving of quantum state during the sampling by the Lyapunov control method are discussed.

A different strategy is proposed to control decoherence from fluctuating magnetic field by adjusting external controllable parameters. The results show that the output states in terms of the fidelity are pure states, which correspond to the state vectors that are given by a renormalized Hamiltonian. Thus, the output states may perfectly preserve memory of initial single-qubit states at some critical magnetic field parameters.

In the Born-Markov approximation and two-level approximation, and using the Bloch-Redfield equation, the decoherence property of superconducting quantum circuit with a flux qubit is investigated. The influence on decoherence of the mutual inductance coupling between the circuit components is complicated. The mutual inductance coupling between different loops will decrease the decoherence time. However, the mutual inductance coupling of the same loop, in a certain interval, will increase the decoherence time. Therefore, we can control the decoherence time by changing the mutual inductance parameters such as the strength and direction of coupling.

In the Born–Markov approximation, decoherence property of superconducting quantum circuit with a flux qubit is investigated. Using Kirchhoff's laws of classical circuit and quantum theory, we derive a Hamiltonian of the circuit. Then, combining with the Bloch–Redfield equation and in the two-level approximation, the energy relaxation time and the decoherence time of superconducting qubits is studied. Compared to the spin-boson model, this method not only investigates a decoherence being caused by the dissipative environment, but also the decoherence being generated by the dissipative elements in a superconducting electronic circuit. Hence, it is good for studying the decoherence of superconducting qubits.

In the Born-Markov approximation, a method that calculates the energy relaxation time T 1 and the decoherence time T 2 of superconducting qubits is given by solving the set of Bloch-Redfield equations and considering the results of decoherence of a superconducting charge qubit. Compared to the spin-boson model, it not only contains the decoherence being caused by the dissipative environment, but also includes the decoherence being generated by the dissipative elements in a superconducting electronic circuit. Hence, it is good for studying the decoherence of superconducting qubits comprehensively.

Utilizing the method of optimal control, we investigated the tactics of decoherence suppression in the open quantum circuit system containing superconducting qubits. We first discussed the modeling of the system under the optimal control. Then, we designed a control law by means of optimal control. The simulation results indicate that the flip time of qubits can be effectively manipulated through changing the weight coefficients of the cost function, which provides a new way for manipulating the decoherence.