Quantum discord and its dynamics for multipartite systems

Quantum discord, one of the famous quantum correlations, has been recently generalized to multipartite systems by Radhakrishnan et al. Here we give analytical solutions of the quantum discord for a family of N-qubit quantum states. For the bipartite system, we derive a zero quantum discord which will remain unchanged under the phase damping channel. For multiparitite systems, it is found that the quantum discord can be classified into three categories and the quantum discord for odd-partite systems can exhibit freezing under the phase damping channel, while the freezing does not exist in the even-partite systems.

Pure State Feedback Switching Control Based on the Online Estimated State for Stochastic Open Quantum Systems

For the n-qubit stochastic open quantum systems,based on the Lyapunov stability theorem and LaSalle’s invariant set principle,a pure state switching control based on on-line estimated state feedback(short for OQST-SFC)is proposed to realize the state transition the pure state of the target state including eigenstate and superposition state.The proposed switching control consists of a constant control and a control law designed based on the Lyapunov method,in which the Lyapunov function is the state distance of the system.The constant control is used to drive the system state from an initial state to the convergence domain only containing the target state,and a Lyapunov-based control is used to make the state enter the convergence domain and then continue to converge to the target state.At the same time,the continuous weak measurement of quantum system and the quantum state tomography method based on the on-line alternating direction multiplier(QST-OADM)are used to obtain the system information and estimate the quantum state which is used as the input of the quantum system controller.Then,the pure state feedback switching control method based on the on-line estimated state feedback is realized in an n-qubit stochastic open quantum system.The complete derivation process of n-qubit QST-OADM algorithm is given;Through strict theoretical proof and analysis,the convergence conditions to ensure any initial state of the quantum system to converge the target pure state are given.The proposed control method is applied to a 2-qubit stochastic open quantum system for numerical simulation experiments.Four possible different position cases between the initial estimated state and that of the controlled system are studied and discussed,and the performances of the state transition under the corresponding cases are analyzed.

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.

Quantum Computation with Two-Level Systems in Current-Biased Josephson Junction

We present a feasible scheme that realizes quantum computation using the two-level systems （TLSs） in Current-biased Josephson junction （CBJJ） under the present experimental technology. Effective manipulation of the TLSs by CBJJ serving as register qubit can be obtained, such as initialization, single-qubit rotations, two-qubit gates, entanglement generation, and read out, etc. In addition, we also discuss the experimental feasibility and efficiency of the scheme.

Establishing formal state space models via quantization forquantum control systems

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrdinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems, such as momentum, energy and Hamiltonian, so Schrdinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrdinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.

Weak-Coupling Theory for Semiclassical Periodically Driven Two-Level Systems： Beyond Rotating-Wave Approximation

We present a weak-coupling theory of semiclassical periodically driven two-level systems. The explicit analytical approximating solution is shown to reproduce highly accurately the exact results well beyond the regime of the rotating-wave approximation.

Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

Rise of quantum correlations in non-Markovian environments in continuous-variable systems

We investigate the time evolution of quantum correlations, which are measured by Gaussian quantum discord in a continuous-variable bipartite system subject to common and independent non-Markovian environments. Considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that quantum correlations can be created during the non-Markovian evolution, which is different from the Markovian process. Furthermore, we find that the temperature is a key factor during the evolution in non-Markovian environments. For common reservoirs, a maximum creation of quantum correlations may occur under an appropriate temperature. For independent reservoirs, the non-Markovianity of the total system corresponds to the subsystem whose temperature is higher. In both common and independent environments, the Gaussian quantum discord is influenced by the temperature and the photon number of each mode.

Controllable Subspaces of Open Quantum Dynamical Systems

This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.

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.

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 phase distribution and the number-phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states：solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.

Entropy of Quantum Dynamical Systems and Sufficient Families in Orthomodular Lattices with Bayessian State

The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.

Quasihole Tunneling in Disordered Fractional Quantum Hall Systems

Fractional quantum Hall systems are often described by model wave functions,which are the ground states of pure systems with short-range interaction.A primary example is the Laughlin wave function,which supports Abelian quasiparticles with fractionalized charge.In the presence of disorder,the wave function of the ground state is expected to deviate from the Laughlin form.We study the disorder-driven colla.pse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state.In particular,we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall （QH） effect on a noncommutative phase space （NCPS）. By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver.

Geometric discord of tripartite quantum systems

We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems,the results presented here show that this property is no longer true in tripartite systems.Furthermore,we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination,that is,we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement.Lastly,we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence.It is interesting that the frozen phenomenon exists for geometric discord in this scenario.

Preface to the Special Issue on Quantum Transport in Mesoscopic Systems

Mesoscopic systems,including nanowires,quantum dots and two-dimensional electron gases,are excellent platforms for studying emerging quantum phenomena,especially in the field of electrical transport.Quantum transport covers vast scopes of condensed matter physics,such as superconductivity,quantum Hall effect,and many investigations in mesoscopic devices.

Rapid stabilization of stochastic quantum systems in a unified framework

Rapid stabilization of general stochastic quantum systems is investigated based on the rapid stability of stochastic differential equations.We introduce a Lyapunov-LaSalle-like theorem for a class of nonlinear stochastic systems first,based on which a unified framework of rapidly stabilizing stochastic quantum systems is proposed.According to the proposed unified framework,we design the switching state feedback controls to achieve the rapid stabilization of singlequbit systems,two-qubit systems,and N-qubit systems.From the unified framework,the state space is divided into two state subspaces,and the target state is located in one state subspace,while the other system equilibria are located in the other state subspace.Under the designed state feedback controls,the system state can only transit through the boundary between the two state subspaces no more than two times,and the target state is globally asymptotically stable in probability.In particular,the system state can converge exponentially in(all or part of)the state subspace where the target state is located.Moreover,the effectiveness and rapidity of the designed state feedback controls are shown in numerical simulations by stabilizing GHZ states for a three-qubit system.

Measure synchronization in hybrid quantum-classical systems

Measure synchronization in hybrid quantum-classical systems is investigated in this paper.The dynamics of the classical subsystem is described by the Hamiltonian equations,while the dynamics of the quantum subsystem is governed by the Schr¨odinger equation.By increasing the coupling strength in between the quantum and classical subsystems,we reveal the existence of measure synchronization in coupled quantum-classical dynamics under energy conservation for the hybrid systems.