Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum correlation.Nonetheless,this indistinguishability is no longer holds for mixed states.To contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum correlations.Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping process.this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes.The key ingredient in analyzing quantum correlation in this system is the global covariance matrix.It forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,respectively.Our study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.

Monogamy of quantum correlations in the one-dimensional anisotropic XXXYYY model

In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with stag- gered Dzyaloshinskii-Moriya （DM） interaction have been investigated using the quantum renormalization group （QRG） method. We summarize the monogamy relation for different quantum correlation measures and make an explicit compar- ison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.

Comparison and control of the robustness between quantum entanglement and quantum correlation in an open quantum system

revised manuscript received 30 April 2012） We investigate the influence of environmental decoherence on the dynamics of a coupled qubit system and quantum correlation. We analyse the relationship between concurrence and the degree of initial entanglement or the purity of initial quantum state, and also their relationship with quantum discord. The results show that the decrease of the purity of an initial quantum state can induce the attenuation of concurrence or quantum discord, but the attenuation of quantum discord is obviously slower than the concurrence＇s, correspondingly the survival time of quantum discord is longer. Further investigation reveals that the robustness of quantum discord and concurrence relies on the entanglement degree of the initial quantum state. The higher the degree of entanglement, the more robust the quantum discord is than concurrence. And the reverse is equally true. Birth and death happen to quantum discord periodically and a newborn quantum discord comes into being under a certain condition, so does the concurrence.

Conservation issue of pairwise quantum discord and entanglement of two coupled qubits in a two-mode vacuum cavity

The conservation issues of pairwise quantum discord and entanglement of two qubits coupled to a two-mode vacuum cavity are investigated by considering the dipole^tipole interaction between two qubits. It is found that the sum of the square of the pairwise quantum discords and the sum of the square of the pairwise concurrences are both conserved in the strong dipole-dipole interaction limit. However, in the middle dipole-dipole and weak dipole-dipole interaction limits, the sum of the square of the pairwise concurrences is still conserved while the sum of the square of the pairwise discords is not. The crucial reason for this is that the quantum discords are not equivalent if the measurements are performed on different subsystems in a general situation. So it is very important for quantum computation depending on the quantum discord to select the target performed by the measurements.

Investigations into quantum correlation of coupled qubits in a squeezed vacuum reservoir

In this paper,we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in a squeezed vacuum reservoir.We compare and analyze the effects of squeezed parameters on quantum discord and quantum concurrence.The results show that in a squeezed vacuum reservoir,the quantum discord and quantum concurrence perform with completely opposite behaviors with the change of squeezed parameters.Quantum discord survives longer with the increase of squeezed amplitude parameter,but entanglement death is faster on the contrary.The results also indicate that the classical correlation of the system is smaller than quantum discord in a vacuum reservoir,while it is bigger than quantum discord in a squeezed vacuum reservoir.The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments,which indicates that the entanglement actually is easily affected by decoherence and quantum discord has a stronger ability to avoid decoherence in a squeezed vacuum reservoir.

Research on the Freezing Phenomenon of Quantum Correlation by Machine Learning

Quantum correlation shows a fascinating nature of quantum mechanics and plays an important role in some physics topics,especially in the field of quantum information.Quantum correlations of the composite system can be quantified by resorting to geometric or entropy methods,and all these quantification methods exhibit the peculiar freezing phenomenon.The challenge is to find the characteristics of the quantum states that generate the freezing phenomenon,rather than only study the conditions which generate this phenomenon under a certain quantum system.In essence,this is a classification problem.Machine learning has become an effective method for researchers to study classification and feature generation.In this work,we prove that the machine learning can solve the problem of X form quantum states,which is a problem of physical significance.Subsequently,we apply the density-based spatial clustering of applications with noise(DBSCAN)algorithm and the decision tree to divide quantum states into two different groups.Our goal is to classify the quantum correlations of quantum states into two classes:one is the quantum correlation with freezing phenomenon for both Rènyi discord(α=2)and the geometric discord(Bures distance),the other is the quantum correlation of non-freezing phenomenon.The results demonstrate that the machine learning method has reasonable performance in quantum correlation research.

Quantum correlation of a three-particle-class state under quantum decoherence

We investigate the quantum characteristics of a three-particle W-class state and reveal the relationship between quan- tum discord and quantum entanglement under decoherence. We can also identify the state for which discord takes a maximal value for a given decoherence factor, and present a strong bound on quantum entanglement-quantum discord. In contrast, a striking result will be obtained that the quantum discord is not always stronger than the entanglement of formation in the case of decoherence. Furthermore, we also theoretically study the variation trend of the monogamy of quantum correlations for the three-particle W-class state under the phase flip channel, and find that the three-particle W-class state could transform from polygamous into monogamous, owing to the decoherence.

Thermal quantum correlations of a spin-1/2 Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya interaction

We investigate the properties of thermal quantum correlations in an infinite spin-1/2 Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya（DM） interaction. The thermal quantum discord（TQD） and the thermal entanglement（TE）are discussed as two kinds of important methods to measure the quantum correlation, respectively. It is found that DM interaction plays an important role in the thermal quantum correlations of the system. It can enhance the thermal quantum correlations by increasing DM interaction. Furthermore, the thermal quantum correlations can be promoted by tuning the external magnetic field and the Heisenberg coupling parameter in the antiferromagnetic system. It is shown that the behaviors of TQD differ from those of TE. TQD is more robust against decoherence than TE. For the measurement of TQD, the ＂regrowth＂ phenomenon occurs in the ferromagnetic system. We also find that the anisotropy favors the thermal quantum correlations of the system with weak DM interaction.

Creation of quantum correlations via the initial classical-mixed states

Using the pseudomode method, we theoretically analyze the creation of quantum correlations between two two-level dipole-dipole interacting atoms coupled with a common structured reservoir with different coupling strengths. Considering certain classes of initial separable-mixed states, we demonstrate that the sudden birth of atomic entanglement as well as the generation of stationary quantum correlations occur. Our results also suggest a possible way to control the occurrence time of entanglement sudden birth and the stationary value of quantum correlations by modifying the initial conditions of states, the dipole-dipole interaction, and the relative coupling strength. These results are helpful for the experimental engineering of entanglement and quantum correlations.

Total Pairwise Quantum Correlation and Entanglement in a Mixed-Three-Spin Ising-XY Model with Added Dzyaloshinskii-Moriya Interaction under Decoherence

We investigate the behavior of geometric global quantum discord （GGQD） and concurrence （C） between half- spins of a mixed-three-spin （1/2, 1, 1/2） system with the Ising-XY model for which spins （1, 1/2） have the Ising interaction and half-spins （1/2, 1/2） have both XY and the Dzyaloshinskii Moriya interactions together, under the decoherence action. A single-ion anisotropy property with coefficient ζ is assumed for the spin-integer. This system which includes an analytical Hamiltonian is considered at the front of an external homogeneous magnetic field B in thermal equilibrium. Finally, we compare GGQD and C and express some interesting phase flip reactions of the total quantum correlation and pairwise entanglement between spins （1/2, 1/2）. Generally, we conclude that the concurrence and GGQD have different behaviors under the phase flip channel.

Geometrical quantum discord and negativity of two separable and mixed qubits

We studied quantum correlation and quantum entanglement of a quantum system in which a coherent state light field interacts with two qubits that are initially prepared in a separable and mixed state.The influence of mean photon number of the coherent field and distribution probability of the atom on the geometrical quantum discord and the negativity are discussed.Our results show that the mean photon number of light field and distribution function of the atom can regulate and control the quantum correlation and quantum entanglement.

Quantum correlations between two non-interacting atoms under the influence of a thermal environment

By considering a double Jaynes-Cummings model, we investigate the dynamics of quantum correlations, such as the quantum discord and the entanglement, for two atoms in their respective noisy environments, and study the effect of the purity and the cavity temperature on the quantum correlations. The results show that the entanglement suffers sudden death and revival, however the quantum discord can still reveal the quantum correlations between the two atoms in the region where the entanglement is zero. Moreover, when the temperature of each cavity is high the entanglement dies out in a short time, but the quantum discord still survives for quite a long time. It means that the quantum discord is more resistant to environmental disturbance than the entanglement at higher temperatures.

Control of sudden transition between classical and quantum correlations of two strongly driven atoms in dissipative cavities

We investigate analytically the dynamics of classical and quantum correlations between two strongly driven atoms, each of which is trapped inside a dissipative cavity. It is found that there exists a finite time interval during which the quantum discord initially prepared in the X-type states is not destroyed by the decay of the cavities. The sudden transition between classical correlation and quantum discord is sensitive to the initial-state parameter, the cavity decay rate, and the cavity mode-driving field detuning. Interestingly, we show that the transition time can be prolonged significantly by increasing the degree of the detuning.

Property of Quantum Correlations with Correlated Noise

我们分析古典并且有相关噪音的标准和所谓的 quasiclassical 动摇隧道和 non-Markovian dephasing 隧道的量关联性质，明确地，我们使用量不一致，纠纷，和导致测量的骚乱(中间) 测量量关联。为动摇隧道，我们发现记忆效果比纠纷在 MID 和量不一致上有更多的影响。为 dephasing 隧道，我们证明 non-Markovian dephasing 隧道是比对 decoherence 的 Markovian dephasing 隧道更柔韧的。我们也发现那起初中间并且量不一致拿不同价值，然后在一特定的时间以后，他们将几乎 monotonically 收进一样的价值和两个腐烂。

Optimizing quantum correlation dynamics by weak measurement in dissipative environment

We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death （ESD） in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement, therefore in this case the entanglement cannot be optimized in the evolution process.

Quantum correlation dynamics in a two-qubit Heisenberg XY Z model with decoherence

Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated by making use of concurrence C and quantum discord （QD）. Firstly, we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented： there is an ＂entanglement intermittently sudden death＂ phenomenon in the concurrence but not in the QD, which is valid for all the initial states of this system. Also, the interval time of entanglement sudden death is found to be strongly dependent on the initial states, the inhomogeneous magnetic field b and the anisotropic parameter △. Then, it implies that the steady concurrence and QD can be obtained in the long-time limit, which means that the environmental decoherence cannot entirely destroy the quantum correlation, the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot. In addition, based on the analysis of the steady concurrence and QD with t →∞, we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and .4, whereas the parameter b is independent of the steady concurrence and QD.

Continuous-Variable Quantum Network Coding Based on Quantum Discord

Establishing entanglement is an essential task of quantum communication technology.Beyond entanglement,quantum discord,as a measure of quantum correlation,is a necessary prerequisite to the success of entanglement distribution.To realize efficient quantum communication based on quantum discord,in this paper,we consider the practical advantages of continuous variables and propose a feasible continuous-variable quantum network coding scheme based on quantum discord.By means of entanglement distribution by separable states,it can achieve quantum entanglement distribution from sources to targets in a butterfly network.Compared with the representative discrete-variable quantum network coding schemes,the proposed continuous-variable quantum network coding scheme has a higher probability of entanglement distribution and defends against eavesdropping and forgery attacks.Particularly,the deduced relationship indicates that the increase in entanglement is less than or equal to quantum discord.

Quantum correlations in a chain-type quantum network

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some observers.In this paper,we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameterλ.The expressions of all post-measurement states between any two observers are obtained,and their quantifications of Bell nonlocality,Einstein-Podolsky-Rosen steering and entanglement with different ranges ofλare respectively detected and analyzed.

Role of Covariance Correlation Tensor in Establishment of Criterion of Quantum Entanglement

This article discusses the role of covariance correlation tensor in the establishment of the criterion of quantum entanglement. It gives a simple example to show the powerfulness in the treatment of quantum dense coding,and illustrates the fact that this method also provides theoretical basis for establishing corresponding knotted pictures.

Criterion of Quantum Entanglement and the Covariance Correlation Tensor in the Theory of Quantum Network

This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of m≥3 nodes.