QUANTUM COMODULE APPROACH THE SOLUTION OF THE QUANTUM YANG-BAXTER EQUATION

In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible to give some set-theoretical solutions of the Quantum Yang-Baxter Equation.

The Singular Upper Triangle Type Solutions with Spin 1/2 of Quantum Yang-Baxter Equation （Ⅱ）

In these two papers (Ⅰ) and (Ⅱ),the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given.In the Paper (Ⅱ),we give the general solutions of the Yang-Baxter equation in this case.

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.

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.

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 Discord in Two-Qubit System Constructed from the Yang-Baxter Equation

Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way,we investigate the quantum discord of the two-qubit system constructed from the Yang–Baxter Equation. The density matrix of this system is generated through the unitary Yang–Baxter matrix R. The analytical expression and numerical result of quantum discord and geometric measure of quantum discord are obtained for the Yang–Baxter system. These results show that quantum discord and geometric measure of quantum discord are only connect with the parameter θ,which is the important spectral parameter in Yang–Baxter equation.

Quasi-linear Cycle Sets and the Retraction Problem for Set-theoretic Solutions of the Quantum Yang-Baxter Equation

Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abelian group structure. Etingof et al. introduced affine Yang-Baxter maps. These are equivalent to cycle sets with a specific abelian group structure. Abelian group structures have also been essential to get partial results for the still unsolved retraction problem. We introduce two new classes of cycle sets with an underlying abelian group structure and show that they can be transformed into each other while keeping the group structure fixed. This leads to a proper extension of the retractibility conjecture and new evidence for its truth.

QUANTUM DOUBLE CONSTRUCTION OF NEW SOLUTIONS TO THE QUANTUM YANG-BAXTER EQUATION

By establishing a new Hopf algebra and the corresponding quantum double,we construct a new universal.R-matrix. Under concrete representations, it produces a family of new solutions to the quantum Yang-Baxter equation without a parameter,in which the so-called non-standard solution associated with the Lie algebra sl(3)is included.

Operational effects of the UNOT gate on classical and quantum correlations

The NOT gate that flips a classical bit is ubiquitous in classical information processing.However its quantum analogue,the universal NOT(UNOT) gate that flips a quantum spin in any alignment into its antipodal counterpart is strictly forbidden.Here we explore the connection between this discrepancy and how UNOT gates affect classical and quantum correlations.We show that while a UNOT gate always preserves classical correlations between two spins,it can non-locally increase or decrease their shared discord in ways that allow violation of the data processing inequality.We experimentally illustrate this using a multi-level trapped ^(171)Yb^+ ion that allows simulation of anti-unitary operations.

Quantum correlations relativity for continuous variable systems

It is shown that a choice of degrees of freedom of a bipartite continuous variable system determines the amount of non-classical correlations (quantified by discord) in the system's state. Non-classical correlations (that include entanglement as a special kind of correlations) are ubiquitous for such systems. For a quantum state, if there are not non-classical correlations (quantum discord is zero) for one, there are in general non-classical correlations (quantum discord is non-zero) for another set of the composite system's degrees of freedom. The physical relevance of this "quantum correlations relativity" is emphasized also in the more general context.

THE DIFFERENTIAL REALIZATION OF NEW SOLUTIONS FOR YANG-BAXTER EQUATION

I. INTRODUCTION Yang-Baxter equation plays a crucial role in the nonlinear integrable system. Its standard solutions can be constructed in terms of the universal R-matrix and representations of the corresponding quantum universal enveloping algebra (or called quantum algebra for short),

Quantum Correlations in a Family of Two-Qubit Separable States

Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four diferent approaches,namely,quantum discord[Phys.Rev.Lett.88(2002)017901],measurementinduced disturbance(MID)[Phys.Rev.A 77(2008)022301],ameliorated MID[J.Phys.A:Math.Theor.44(2011)352002]and quantum dissonance[Phys.Rev.Lett.104(2010)080501].Quantum correlations captured with diferent approaches are compared and discussed so that their three distinct features are exposed.

Characterizing Quantum Correlations in Arbitrary-Dimensional Bipartite Systems Using Hurwitz＇s Theory

Quantum correlations play vital roles in the quantum features in quantum information processing tasks.Among the measures of quantum correlations, quantum discord(QD) and entanglement of formation(EOF) are two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of characterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in arbitrary-dimensional bipartite quantum systems in terms of Hurwitz's theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of arbitrary-dimensional bipartite quantum states via purification, and the relationship between QD and EOF.

Pairwise Quantum Correlations for Superpositions of Dicke States

Pairwise correlation is really an important property for multi-qubit states.For the two-qubit X states extracted from Dicke states and their superposition states,we obtain a compact expression of the quantum discord by numerical check.We then apply the expression to discuss the quantum correlation of the reduced two-qubit states of Dicke states and their superpositions,and the results are compared with those obtained by entanglement of formation,which is a quantum entanglement measure.

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.

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.

Off-diagonal approach to the exact solution of quantum integrable systems

We investigate the t–W scheme for the anti-ferromagnetic X X X spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated W operator(see Eqs.(10) and(70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of W operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation(the t–W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

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.

Effectiveness of Non-Markovian Methods for Quantum Discord Dynamics of Non-coupled Two-Qubit System

The dissipative dynamics of non-coupled two qubits interacting with independent reservoir is studied by solving the non-Markovian master equation. In order to examine the effectiveness of the Nakajima-Zwanzig and timeconvolutionless master equations in the description of quantum correlation dynamics, different coupled regimes are investigated. The comparison between the above two master equation methods for investigating the dynamics of quantum discord is also made. Finally, we further confirm that the two master equations should be applied in different regimes of qubits coupled to their reservoirs, respectively.

量子Yang-Baxter方程的1/2旋子的奇异上三角型解(Ⅰ)(英文)

In these two papers (I) and (II), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (I), we give the Yang-Baxter equation and give the general solutions of some function equations for the next paper.