Behavior Of Quantum Correlations Research Articles

Schwinger–Keldysh Path Integral Formalism for a Quenched Quantum Inverted Oscillator

In this work, we study the time-dependent behavior of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger–Keldysh formalism in the presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstate and continuous energy eigenvalues. Using the expression for the eigenstate, we further derive the most general expression for the generating function as well as the out-of-time-ordered correlators (OTOCs) for the given system using this formalism. Further, considering the time-dependent coupling and frequency of the quantum inverted oscillator characterized by quench parameters, we comment on the dynamical behavior, specifically the early, intermediate and late time-dependent features of the OTOC for the quenched quantum inverted oscillator. Next, we study a specific case, where the system of an inverted oscillator exhibits chaotic behavior by computing the quantum Lyapunov exponent from the time-dependent behavior of OTOCs in the presence of the given quench profile.

Quantum correlations and coherence in a mixed spin- (12,1) Heisenberg dimer under intrinsic decoherence

This research delves into the dynamical behavior of quantum correlations and coherence within a mixed Heisenberg dimer system under the intrinsic decoherence. Our approach involves the application of logarithmic negativity, local quantum uncertainty, and the ℓ 1 norm-based coherence as quantifiers for entanglement, skew information correlations, and quantum coherence in this qubit-qutrit model. Our primary objective is to explore the impact of various factors on the dynamics of quantum correlations and quantum coherence. These factors encompass the initial density matrix and its mixing parameter, the intrinsic decoherence rate (γ), the external magnetic field, as well as intrinsic system parameters, notably the XXZ and uniaxial single-ion anisotropies. Our results demonstrate that the introduction of intrinsic decoherence (ID) significantly erodes quantum resources. Particularly, for high values of the ID rate (γ), excessive damping occurs, leading to the absence of oscillations or a rapid decay of quantum resources, ultimately stabilizing in steady states. Furthermore, the presence of an external homogeneous magnetic field further diminishes quantum resources within the system. However, despite the degradation induced by the combined influence of intrinsic decoherence and high external magnetic field intensities, the judicious selection of the initial density matrix and precise adjustment of the uniaxial single-ion anisotropy enable the preservation of quantum resources within the mixed spin-(1/2, 1) Heisenberg dimer.

Effects of intrinsic decoherence on quantum coherence and correlations between spins within a two-dimensional honeycomb lattice graphene layer system

This research delves into the influence of intrinsic decoherence on the behavior of quantum correlations and coherence between two interacting qubits in a graphene-based system. To evaluate the amount of nonclassical correlations in the system, we employ local quantum uncertainty (LQU), and to assess quantum coherence we use the relative entropy of coherence [Formula: see text] and [Formula: see text]-norm [Formula: see text]. We assume that the system is initially prepared in an extended-Werner-like (EWL) state, and we investigate how these quantifiers evolve over time and examine their sensitivity to various graphene layer system parameters, mixture parameter of the initial state and the intrinsic decoherence rate. Our results indicate that by adjusting the wave number operators, decreasing the intrinsic decoherence rate, and increasing the initial state mixing parameter, it is possible to enhance both quantum correlations and coherence within the two-dimensional honeycomb lattice system. In addition, we found that quantum coherence is more resilient to intrinsic decoherence than LQU, moreover, the [Formula: see text]-norm is more robust than the relative entropy of coherence.

Local Quantum Uncertainty and Quantum Interferometric Power in an Anisotropic Two-Qubit System

Investigating the favorable configurations for non-classical correlations preservation has remained a hotly debated topic for the last decade. In this regard, we present a two-qubit Heisenberg spin chain system exposed to a time-dependent external magnetic field. The impact of various crucial parameters, such as initial strength and angular frequency of the external magnetic field along with the state’s purity and anisotropy of the spin-spin on the dynamical behavior of quantum correlations are considered. We utilize local quantum uncertainty (LQU) and quantum interferometric power (QIP) to investigate the dynamics of quantum correlations. We show that under the critical angular frequency of the external magnetic field and the spin-spin anisotropy, quantum correlations in the system can be successfully preserved. LQU and QIP suffer a drop as the interaction between the system and field is initiated, however, are quickly regained by the system. This tendency is confirmed by computing a measure of non-classical correlations according to the Clauser–Horne–Shimony–Holt inequality. Notably, the initial and final preserved levels of quantum correlations are only varied when variation is caused in the state’s purity.

Entangled multiplets and spreading of quantum correlations in a continuously monitored tight-binding chain

We analyze the dynamics of entanglement in a paradigmatic noninteracting system subject to continuous monitoring of the local excitation densities. Recently, it was conjectured that the evolution of quantum correlations in such system is described by a semi-classical theory, based on entangled pairs of ballistically propagating quasiparticles and inspired by the hydrodynamic approach to unitary (integrable) quantum systems. Here, however, we show that this conjecture does not fully capture the complex behavior of quantum correlations emerging from the interplay between coherent dynamics and continuous monitoring. We unveil the existence of multipartite quantum correlations which are inconsistent with an entangled-pair structure and which, within a quasiparticle picture, would require the presence of larger multiplets. We also observe that quantum information is highly delocalized, as it is shared in a collective {\it nonredundant} way among adjacent regions of the many-body system. Our results shed new light onto the behavior of correlations in quantum stochastic dynamics and further show that these may be enhanced by a (weak) continuous monitoring process.

Weak Measurement Effects on Dynamics of Quantum Correlations in a Two-Atom System in Thermal Reservoirs

The dynamical behavior of quantum correlations captured by different forms Measurement-Induced Nonlocality (MIN) between two atoms coupled with thermal reservoirs is investigated and compared with the entanglement. It is shown that the MIN quantities are more robust, while noise causes sudden death in entanglement. Further, we quantified the quantum correlation with weak measurement, and the effect of measurement strength is observed. The role of mean photon number and weak measurement on quantum correlation is also highlighted.

Behavior of quantum discord, local quantum uncertainty, and local quantum Fisher information in two-spin-1/2 Heisenberg chain with DM and KSEA interactions

A two-qubit Heisenberg XYZ model with Dzyaloshinsky–Moriya (DM) and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interactions is considered at thermal equilibrium. Analytical formulas are derived for the local quantum uncertainty (LQU) and local quantum Fisher information (LQFI). Using the available expressions for the entropic quantum discord, we perform a comparative study of these measures of nonclassical correlation. Our analysis showed the following: all three measures of quantum correlation have similar qualitative and even quantitative behavior on temperature for different values of system parameters, there are regions in the parameter space correspondent to a local increase of correlations with increasing temperature, and sudden changes in the behavior of quantum correlations occur at certain values of the interaction parameters.

Landau-type sudden transitions of quantum correlations

Sudden changes of quantum correlations in the Bell-diagonal states are well-known effects. They occur when the set of optimal parameters that determine the quantum correlation consists of isolated points and optimal parameters during the evolution of the system jump from one such point to another (e.g., the optimal measurement angle of the quantum discord changes discontinuously from zero to π/2 or vice versa). However, when considering more general X quantum states, we found that quantum discord and one-way quantum work deficit can experience sudden changes of other kinds. Namely, the optimal measurement angle may suddenly start to shift continuously from its stationary value 0 or π/2 to an intermediate optimal measurement angle ϑ ∈ (0, π/2). This leads to a new behavior of quantum correlations, which is mathematically described by the Landau phenomenological theory of second-order phase transitions. In addition, for the one-way quantum work deficit, we found cases where the optimal measurement angle jumps from zero to a nonzero step less than π/2, and then continuously changes its value. This behavior of quantum correlation is similar to a first-order phase transition in Landau’s theory. Dependencies of quantum discord and one-way quantum work deficit near the boundaries, which separate regions with state-dependent (variable) and state-independent (stationary, constant) optimal measurement angles, are examined in detail on an example of the XXZ spin model in an external field at thermal equilibrium.

Signatures of intrinsic decoherence and weak measurement on quantum correlations

In this article, we consider a pair of spin-1/2 particles with squeezing coupling serving as the physical carrier of quantum information. We then examine the dynamics of quantum correlation quantified by the entanglement and measurement-induced nonlocality (MIN) under the intrinsic decoherence. The impact of intrinsic decoherence on the dynamical behaviors of quantum correlations is investigated. We show that the MIN quantities are more robust, while intrinsic decoherence cause sudden death in entanglement. Besides, we highlight the role of spin squeezing coupling and external magnetic field on quantum correlation measures. Finally, we investigate the impact of weak measurement on MIN.

Global quantum discord in the Lipkin–Meshkov–Glick model at zero and finite temperatures

We study the global quantum discord (GQD) in the Lipkin–Meshkov–Glick (LMG) model at zero and finite temperatures, in which all spins are mutually interacted and introduced in an external magnetic field (denoted by h). We confirm that the high coordinate number is one of the most distinguishing features of the LMG model, which directly results in the nontrivial behaviors of quantum correlations. We compare the GQD with other quantum correlations measures (such as concurrence, quantum discord, and global entanglement) and find the remarkable difference between them. For instance, we find that GQD spreads in the entire system and captures more information on quantum correlations when comparing with concurrence and quantum (pairwise) discord. We discover that GQD can characterize multipartite correlations in the both broken phase (h < 1) and the symmetric phase (h ⩾ 1), while global entanglement and its generalized fail. Moreover, we show that the ground-state GQD can identify second-order quantum phase transitions of the LMG model in the thermodynamic limit. By making the scaling behavior of the GQD in the LMG model analysis, we show that GQD (denoted by ) scales as with k > 0 in the anisotropic cases for any fixed magnetic field. We further show that GQD behaves as with k < 0 in the isotropic cases for any Dicke state |s n ⟩. Herein k and c are the fitting parameters. We also find that the thermal stability of the GQD at low temperatures depends on the energy gap. We further reveal that the extraordinary behaviors of the thermal-state GQD in the isotropic LMG model are explained by the contribution theory of the energy levels.

Robustness of Measurement–Induced Correlations Under Decoherence Effect

In this article, we study the dynamics of quantum correlation measures such as entanglement and measurement–induced nonlocality (MIN). Starting from an arbitrary Bell-diagonal mixed state under Markovian local noise such as bit-phase flip, depolarizing and generalized amplitude damping channel, we provide the decays of the entanglement measured by concurrence and quantum correlation captured by different forms of MIN (trace distance, Hilbert–Schmidt norm and relative entropy) as a function of the decoherence parameters. The effect of local noises on the dynamical behaviors of quantum correlation is also observed. We show the existence of specific and important features of MIN such as revival, noise robustness and sudden change with respect to decoherence parameter. It is observed that all the noises cause sudden death of entanglement for partially entangled states. Further, we show the existence of separable quantum states with non-zero quantum correlations in terms of MIN.

Sudden change of local quantum uncertainty and geometry for arbitrary two-qubit X-states

Local quantum uncertainty (LQU) as a reliable measure of nonclassical correlations has been recently proposed by Girolami et al. (Phys Rev Lett 110:240402, 2013). In this paper, we have derived an explicit analytical expression of LQU and presented the level surfaces of constant LQU for a class of two-qubit X-states beyond Bell-diagonal states. The dynamical behavior of quantum correlations via the LQU under decoherence environment is studied, and the phenomenon of a sudden change of LQU is demonstrated. Our results are illustrated through the action of different noisy environments individually on a single qubit of quantum system where there is a necessary condition for the occurrence of sudden change of LQU.

Quantum correlations dynamics in two coupled semiconductor InAs quantum dots

We investigate the dynamics of both quantum discord and concurrence within two excitonic qubits embedded in two coupled semiconductor quantum dots independently interacting with dephasing reservoirs. Their behavior in both Markovian and non-Markovian environments is explored against the dimensionless time and the temperature. Moreover, the effects of the external electric field on these correlations as well as the effects related to the Förster interaction are extensively analyzed. We show that the non-Markovian behavior of quantum correlations is always preserved under the variation of the electric field and the Förster interaction, regardless of the strong influence of these two parameters on the amount of quantum correlations. Furthermore, we show that nonzero discord can still be observed for large values of temperature and dimensionless time, unlike concurrence which vanishes in this regime.

Revisiting the behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

The main aim of this work is to investigate the relation between the freezing of Quantum Discord and the behavior of the actual quantum correlations present in bipartite quantum states. In order to accomplish this objective, we use first the Fano representation of two-qubit states from which we can identify a correlation matrix containing the information about the classical and quantum correlations present in the bipartite quantum state. From the behavior of the elements of the correlation matrix before and after making measurements on one of the subsystems, we identify the classical and quantum correlations present in these bipartite states. Then, we use this correlation matrix as a tool to analyze the phenomenon of non-dissipative decoherence in two-qubit states with maximally mixed marginals in typical dynamic scenarios where freezing of standard Quantum Discord takes place. We find that under some initial conditions where freezing of quantum discord occurs, some quantum correlations instead may not remain constant. In order to further explore into these results we also compute for the first time a recently introduced non-commutativity measure of quantum correlations (NCMQC) to analyze the behavior of quantum correlations under the same scenarios of non-dissipative decoherence. In complete agreement with the results obtained by means of the correlation matrix, our results also show that quantum correlations, as measured by NCMQC, do not freeze. Thus, our results put at stake the usual interpretation that the freezing of Quantum Discord is equivalent to the freezing of the physical quantum correlations themselves. We conclude from our study that freezing of quantum discord may not always be identified as equivalent to the freezing of the actual quantum correlations. Thus, the identification of freezing of quantum discord as a useful resource for tasks of quantum information processing is called into question.

Dynamics of quantum correlation for circularly accelerated atoms immersed in a massless scalar field near a boundary

In this paper, we explore the dynamics of quantum correlation for two circularly accelerated atoms interacting with a bath of fluctuating massless scalar field with a reflecting plane boundary. First, we derive the master equation that governs the system evolution. Then we analyze the behaviors of quantum correlation for various conditions and compare the behaviors of quantum correlation with that of the static atoms immersed in a thermal bath with a boundary. It is found that the dynamics of quantum correlation for circularly accelerated atoms present some features distinct from those of static atoms immersed in a thermal bath.

Quantum correlation affected by quantum gravitational fluctuation

We study the behaviors of quantum correlation for two independent gravitationally polarizable subsystems interacting with fluctuating quantum gravitational field. We firstly derive the master equation that the system evolution obeys. Then we discuss the generation, revival, attenuation and enhancement of quantum correlation, which are dependent on the initial state, separation and polarization of the two subsystems. It is shown that quantum correlation for correlated initial state can be preserved effectively from the quantum gravitational fluctuation when the separation between the two subsystems is sufficiently small. Compared with the entanglement behaviors, it is shown that quantum correlation presents better robustness than entanglement, which may be helpful to quantum information processing. Furthermore, the initial state, separation and polarization of the subsystems give us more freedom to manipulate the behaviors of quantum correlation under quantum gravitational decoherence. Our study would throw light on our exploration of quantum gravity.

Behaviors of quantum correlation for accelerated atoms coupled with a fluctuating massless scalar field with a perfectly reflecting boundary

In this work, we study the dynamics of quantum correlation for two uniformly accelerated atoms immersed in a bath of fluctuating massless scalar field with a perfectly reflecting plane boundary in the Minkowski vacuum. Firstly, the master equation that governs the system evolution is derived. Then we discuss the generation, revival and decay of quantum correlation for initial zero-correlation state and initial entangled state in various conditions and models. We contrast the behaviors of quantum correlation of accelerated atoms with that of static atoms in a thermal bath at the corresponding Unruh temperature and also make a comparison between behaviors of quantum correlation and entanglement behaviors. We find that behaviors of quantum correlation of uniformly accelerated atoms present some features distinct from that of static atoms immersed in a thermal bath, and behaviors of quantum correlation are more robust than that of entanglement.

Behaviors of quantum correlation for atoms coupled with fluctuating electromagnetic field with a perfectly reflecting boundary

We study the behaviors of quantum correlation for two atoms interacted with fluctuating electromagnetic field near a perfectly reflecting boundary. We firstly derive the master equation that governs the system evolution. Then, we discuss the generation, revival and degradation of quantum correlation, which are closely related to boundary effect and atomic polarization direction. Compared with the entanglement behaviors, it is shown that quantum correlation presents better robustness than entanglement, which may be helpful to quantum information processing. Furthermore, the presence of boundary offers us a means for preserving quantum correlation under decoherence and gives us more freedom to adjust the behaviors of quantum correlation.

Robustness of quantum correlation for accelerating two atoms coupled with electromagnetic field

In this paper, we investigate the behaviors of quantum correlation quantified by trace norm measurement-induced nonlocality (TMIN) for two uniformly accelerated atoms coupled with electromagnetic vacuum fluctuation in the Minkowski vacuum. We firstly discuss the solving process of master equation that governs the system evolution based on the Pauli matrix presentation for two-qubit state. Similar to [Y. Q. Yang et al., Phys. Rev. A 94, 032337 (2016)], we analyze the degradation, creation, revival and enhancement of quantum correlation for different initial states and polarizations of two atoms, and the influence of interatomic separation and acceleration on quantum correlation. Compared with the entanglement dynamics discussed in [Y. Q. Yang et al., Phys. Rev. A 94, 032337 (2016)], it is found that quantum correlation exhibits better robustness than entanglement. This may be helpful for quantum information processing.

Dynamical quantum correlations after sudden quenches

We employ the mean-field approach in the fermionic picture of the spin-1/2 XXZ chain to investigate the dynamics of bipartite quantum discord and concurrence under sudden quenching. In the case, when quenching is performed in the anisotropy from an initial value to the critical point, the quantum correlations show periodic cusps in time. Moreover, the first suppression (cusp) in quantum correlations can be explained in terms of the semi-classical picture of quasiparticle propagation. On the other hand, quenching to, as well as away from the criticality point shows that the longtime pairwise quantum discord gets enhanced from its initial state. Finally, we show that in the gapped region a quench in the transverse field displays survival of the next-nearest-neighbor quantum discord. Our results provide a further insight into the dynamical behavior of quantum correlations and their connections to quantum criticality.