Spin-chain Environment Research Articles

Higher order approximations in quantum speed limit time of a qubit coupled to XXZ spin chain environment

Higher order approximations in quantum speed limit time of a qubit coupled to XXZ spin chain environment

Dynamical evolution of the two-qubit system with Ising spin-chain environment

In this article, we study the evolution of the two-qubit system with Ising spin-chain environment by choosing the Lindblad equation to describe this process. First, we expand the Hamiltonian of a two-qubit system with its eigenstates and give the Lindblad equation for the evolution of the two-qubit system with Ising spin-chain as the environment. Compared with directly calculating the differential equation between elements of density matrix, we choose a method to solve the Lindblad equation with a smaller calculation dimension. Finally, by constructing an operator solution with operators, we obtain the dynamics of the two-qubit system with Ising spin-chain environment.

Dynamics of quantum coherence and correlations in a transverse Ising spin chain environment

In this paper, we study the dynamical processes of quantum coherence and correlations for two central qubits system coupled with a transverse Ising spin chain. Suppose the initial state of quantum system is the Werner state and the initial state of environment is the ground state of spin chain, and the corresponding time evolution operator, decoherence factor and reduced density matrix are given. We deduce the analytical expressions of evolution of quantum coherence, entanglement and quantum discord. We find that when the spin chain undergoes quantum phase transition (QPT), the entanglement vanished at time [Formula: see text], and the coherence and discord vanished when the decoherence factor decayed to zero. Besides, we also find that the environmental scale N, coupling strength g and parameter P of Werner state do not change the evolution rules of quantum correlation, but accelerate their decay rate with these parameters’ increase.

Steered coherence of a central two-qubit system coupled to an XY spin chain

We investigate the average steered coherence (ASC) of a central two-qubit system coupled to an XY spin-chain environment. It is shown that there exists subspace in which the initial states are immune to this environment. Outside of this subspace, the decay of the ASC can be significantly suppressed by tuning the interaction of the central qubits and its anisotropy in the z axis, as well as the anisotropy of the spin–spin interaction in the xy plane of the environment and the strength of the transverse magnetic field. For the initial Bell states and their unitary equivalent classes, one can also identify system and environmental parameters for which the ASC oscillates near its maximum even in the long-time interval.

Quantum speed limit and topological quantum phase transition in an extended [formula omitted] model

We explore quantum speed limit time τQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that τQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field λ or the anisotropy γ of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of τQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the three-site interaction α or its anisotropy δ. Additionally, we also investigate τQSL for arbitrary time-evolution state in the whole dynamics process and find that τQSL exhibits a behavior of oscillation at non-critical points. However, τQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points.

Decoherence Induced by a Spin Chain: Role of Initial Prepared States

We study the decoherence process induced by a spin chain environment on a central spin consisting of R spins and we apply it on the dynamics of quantum correlations (QCs) of three interacting qubits. To see the impact of the initially prepared state of the spin chain environment on the decoherence process, we assume the spin chain environment prepared in two main ways, namely, either the ground state or the vacuum state in the momentum space. We develop a general heuristic analysis when the spin chain environment is prepared in these states, to understand the decoherence process against the physical parameters. We show that the decoherence process is mainly determined by the choice of the initially prepared state, the number of spins of the chain, the coupling strength, the anisotropy parameter and the position from the quantum critical point. In fact, in the strong coupling regime, the decoherence process does not appear for the environment prepared in the vacuum state and it behaves oscillatory in the case of evolution from the ground state. On the other hand, in the weak coupling regime and far from the quantum critical point, decoherence induced by the ground state is weaker than that of the vacuum state. Finally, we show that QCs are completely shielded from decoherence in the case of evolution from the W state and obey the same dynamics as the decoherence factors for the GHZ state.

The Dynamics of Quantum-Memory-Assisted Entropic Uncertainty of Two-Qubit System in the XY Spin Chain Environments with Dzyaloshinsky-Moriya Interaction

We investigate the dynamical behaviors of quantum-memory-assisted (QMA) entropic uncertainty for the central two-qubit system coupled to the N-site spin XY chain environment with z-component Dzyaloshinsky-Moriya (DM) interaction and external magnetic field, asymmetrically. The results show that the dynamics of QMA entropic uncertainty for a pair of Pauli observables are oscillatory and ascending gradually with evolution time, which is anti-correlated to the entanglement of the two-qubit system. We also find that QMA entropic uncertainty exhibits sudden change phenomena near the critical point of quantum phase transform both in the case of weak and strong coupling regimes, which can act as a new witness of the critical point of quantum phase transition. Meanwhile, the DM interactions of the spin chain environment have non-equivalent effects on the QMA entropic uncertainty when the external magnetic field strength is far from the critical point. Furthermore, the asymmetricallity of the qubit-environment couplings has slightly effects on QMA entropic uncertainty in the case of strong coupling regime of the two-qubit system. While, in the weak coupling regime of the two-qubit system, QMA entropic uncertainty is very sensitive to the asymmetricallity of qubit-environment couplings. Finally, the larger the number of spin sites of the environment, the more quickly the QMA entropic uncertainty increases to the maximal value both in the weak and strong coupling regimes of the two-qubit system.

Tensor-network-based machine learning of non-Markovian quantum processes

We show how a tensor-network-based machine learning algorithm can learn the structures of generic, non-Markovian, quantum stochastic processes. First, a process is represented as a matrix product operator (MPO) and trained with a database of local input states at different times and the corresponding time-nonlocal output state. We then apply the algorithm to predict the output state of a process at different times for a system that is coupled to a spin-chain environment. We then reconstruct the full process, and we quantify the non-Markovian memory by means of the bond dimension of the MPO for various properties of the system, of the environment, and of their interaction. Our study paves the way for a possible experimental investigation into the process tensor and its properties, and an effective characterization of noise in quantum devices.

Quantum speed limit for a three-qubit system in spin-chain environment with multisite interaction

We study the relationship between the quantum speed limit (QSL) time of a three-qubit system, and the quantum phase transitions (QPTs) of a spin-chain environment with the three-spin interaction. We find that the three-spin interaction can effectively manipulate the critical value of the QSL time. It makes the QSL time mark more clearly the quantum phase transition of the one-dimensional spin-chain models, especially the XX model. The dynamical evolution of the QSL time presents a periodic behavior in quantum-critical environment, whereas the three-spin interaction and external magnetic field can destroy this periodicity.

Dynamics of Einstein-Podolsky-Rosen Steering in Quantum Spin Environment

We explore the dynamics of Einstein-Podolsky-Rosen steering (EPR), measured by steering robustness, for two spin-qubits coupled to a general XY spin chain environment. The evolution process is numerically investigated in the vicinity of critical point for the spin environment. The results show an obvious suppression of steering robustness when the environment undergoes a quantum phase transition. The scaling behavior for the dynamics of EPR steering is also revealed and analyzed around the critical point. Furthermore, we find that steering robustness power (i.e. the average value of steering robustness within a certain time) can indicate the quantum criticality of the environment directly.

Quantum criticality of quantum speed limit for a two-qubit system in the spin chain with the Dzyaloshinsky–Moriya interaction

We study the quantum speed limit (QSL) time of a two-qubit system coupled to a spin–chain model with the Dzyaloshinsky–Moriya (DM) interaction. For the Bell state coupled to the Ising model or anisotropic XY model, we find that there is a prominent corresponding relationship between the QSL time and quantum phase transition in a spin–chain environment with larger scale, and the DM interaction can strongly enhance or suppress the response relation. Remarkably, when the surrounding environment is set to the XX model, the DM interaction makes it possible for us to witness the quantum phase transition by the local anomalous enhancement of the QSL time near the critical point. In addition, our analyses indicate that the entanglement can speed-up the system evolution in many-body environment.

Quantum coherence dynamics of three-qubit states in XY spin-chain environment

We investigate the dynamics of quantum coherence, based on relative entropy and quantum skew information, for tripartite systems in a quantum-critical environment. We demonstrate that initial states, the strength of magnetic field, anisotropy parameter, system–environment coupling, and the scale of the environment strongly affect coherence evolution. We find that two measures of coherence are frozen for the initial W state coupled to an XY spin-chain environment as the system–environment coupling satisfies certain conditions. We compare the dynamics of quantum coherence with that of the entanglement and the quantum discord. The analysis shows no hierarchical relationship among them.

Decoherence for a two-qubit system in a spin-chain environment**Project supported by the National Natural Science Foundation of China (Grant No. 11404246) and the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2017MF040).

The quantum coherence and correlation dynamics for a two-qubit system in the Ising spin-chain environment are studied. A sudden change of coherence is found near the critical point, which provides us with an effective way to detect the quantum phase transition. By studying the relationship between quantum discord and coherence, we find that coherence displays the behavior of classical correlation for t < t0, and of quantum discord for t > t0, where t0 is the time-point of a sudden transition between classical and quantum decoherence.

Frozen Quantum Coherence for a Central Two-Qubit System in a Spin-Chain Environment**Supported by the National Natural Science Foundation of China under Grant No 11404246, and the Shandong Provincial Natural Science Foundation under Grant No ZR2017MF040.

We investigate the dynamics of coherence for a central two-qubit system coupled to an XY spin chain with the Dzyaloshinsky–Moriya interaction. It is found that a sudden transition of coherence exists near the critical point in the weak-coupling case, and an oscillatory envelope appears in the strong-coupling case. In both cases the freezing phenomenon of coherence can be found.

Capacity of a quantum memory channel correlated by matrix product states

We study the capacity of a quantum channel where channel acts like controlled phase gate with the control being provided by a one-dimensional quantum spin chain environment. Due to the correlations in the spin chain, we get a quantum channel with memory. We derive formulas for the quantum capacity of this channel when the spin state is a matrix product state. Particularly, we derive exact formulas for the capacity of the quantum memory channel when the environment state is the ground state of the AKLT model and the Majumdar–Ghosh model. We find that the behavior of the capacity for the range of the parameters is analytic.

Quantum correlations dynamics of three-qubit states coupled to an XY spin chain: Role of coupling strengths☆☆Project supported by National Basic Research Program of China (Grant No. 2013CBA01702) and National Natural Science Foundation of China (Grant Nos. 61377016, 61575055, 10974039, 61307072, 61308017, and 61405056).

We investigate the prominent impacts of coupling strengths on the evolution of entanglement and quantum discord for a three-qubit system coupled to an XY spin-chain environment. In the case of a pure W state, more robust, even larger nonzero quantum correlations can be obtained by tailoring the coupling strengths between the qubits and the environment. For a mixed state consisting of the GHZ and W states, the dynamics of entanglement and quantum discord can characterize the critical point of quantum phase transition. Remarkably, a large nonzero quantum discord is generally retained, while the nonzero entanglement can only be obtained as the system-environment coupling satisfies certain conditions. We also find that the impact of each qubit’s coupling strength on the quantum correlation dynamics strongly depends on the variation schemes of the system-environment couplings.

Interplay between Landau-Zener transition dynamic and quantum phase transition in dissipative spin chain with Dzyaloshinsky-Moriya interaction

The paper investigates the transition dynamic of a two-level system coupled uniformly to a general XY dissipative spin-chain environment with the Dzyaloshinsky-Moriya interaction. The collective effect of the spin-chain environment is studied and we obtained the exact expression of the final occupation of the system. It is observed that the increase of the decay parameter favors a shortcut to adiabaticity. In the absence of decay, the transition probability oscillations are modulated in time by the renormalized Landau-Zener (LZ) parameter that we derived. We found that in the vicinity of the critical point of the environment, depending on the strength of the system-environment coupling, the decay of the population transfer can be tailored by tuning the other parameters of the model. The critical point and thus the occurrence of the phase transition are observed to be independent of these parameters. It is shown that this quantum state transition is related to the occurrence of the quantum phase transitions in the chain. The adiabatic change for the magnetization observed in some magnetic molecules may be due to the number of spin involved in the chain, the anisotropy parameter of the chain or the external magnetic field strength.

Dynamics of Entanglement and Measurement-Induced Disturbance for a Hybrid Qubit-Qutrit System Interacting with a Spin-Chain Environment: A Mean Field Approach

We use the mean field method to study the dynamics of thermal entanglement and also the measurement-induced disturbance for a mixed qutrit-qubit system coupled to an environment, comprised of an Ising spin-chain with long range interactions, embedded in a transverse magnetic field. It is revealed that both quantities die down in long enough time and the fade out time is a decreasing function of temperature; however, the environmental magnetic field holds back the decoherence, and increases the fade out time; thus, providing a means to control and postpone the decoherence process. Moreover, it is observed that the discrepancy between the interaction strength of the qubit and the qutrit with the environment, substantially affects the decoherence behavior of the system.

Single spin probe of many-body localization

We use an external spin as a dynamical probe of many body localization. The probe spin is coupled to an interacting and disordered environment described by a Heisenberg spin chain in a random field. The spin-chain environment can be tuned between a thermalizing delocalized phase and non-thermalizing localized phase, both in its ground- and high-energy states. We study the decoherence of the probe spin when it couples to the environment prepared in three states: the ground state, the infinite temperature state and a high energy N\'eel state. In the non-thermalizing many body localized regime, the coherence shows scaling behaviour in the disorder strength. The long-time dynamics of the probe spin shows a logarithmic dephasing in analogy with the logarithmic growth of entanglement entropy for a bi-partition of a many-body localized system. In summary, we show that decoherence of the probe spin provides clear signatures of many-body localization.

Persistence of quantum correlations in a XY spin-chain environment

Quantum correlations in a physical system are usually degraded whenever there is an interaction with the environment. Here we consider the action of a XY spin-chain interacting with a system of two qubits. Results are surprising for particular families of states since their evolution does not destroy the presence of either entanglement or nonlocality, that is, those correlations persist for any possible configuration of the environment. In addition, we unveil the form of those states which, although being mixed, their entanglement implies nonlocality and vice versa. This finding constitutes an extension of the well-known Gisin Theorem for pure states of two qubits. The ensuing form will enable us to find the evolved entanglement and nonlocality in an analytical fashion.