We examine the entanglement of general mixed states of a two qubit Heisenberg XYZ chain in the presence of a magnetic field, and its detection by means of different criteria. Both the exact separability conditions and the weaker conditions implied by the disorder and the von Neumann entropic criteria are analyzed. The ensuing limit temperatures for entanglement in thermal states of different XYZ models are then examined and compared with the limit temperature of the symmetry-breaking solution in a mean field type approximation. The latter, though generally lower, can also be higher than the exact limit temperature for entanglement in certain cases, indicating that symmetry-breaking does not necessarily entail entanglement. The reentry of entanglement for increasing temperatures is also discussed.
Quantum correlation of bipartite states (beyond entanglement) in presence of environment is studied for Heisenberg XYZ spin system. It is shown that if the system is allowed to exchange energy with environment, the initial state evolves and settles down to uncorrelated state in asymptotic limit. We have also demonstrated that fidelity based measurement induced non-locality is a useful quantity in characterizing correlated quantum states.
In this paper, we study the thermal entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya (DM) couplings. We show that different DM coupling parameters have different influences on the entanglement and the critical temperature. In addition, we find that when $J_{i}$ ($i$-component spin coupling interaction) is the largest spin coupling coefficient, $D_{i}$ ($i$-component DM interaction) is the most efficient DM control parameter, which can be obtained by adjusting the direction of DM interaction.
In this work we will study the Local quantum Fisher information and the local quantum uncertainty in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii Moriya (DM) interaction in z direction. Here we show that the DM interaction and spin interactions along the x, y, and z axis can increase and maintain local quantum Fisher information and local quantum uncertainty. It is also shown that because of thermal fluctuations local quantum Fisher information and local quantum uncertainty are decreased by increasing temperature. They are equal to one at very low temperature and starts to dec…
The thermal entanglement in Heisenberg $XYZ$ chain is investigated in the presence of external magnetic field $B$. In the two-qubit system, the critical magnetic field $B_c$ is increased because of introducing the interaction of the z-component of two neighboring spins $J_z$. This interaction not only improves the critical temperature $T_c,$ but also enhances the entanglement for particular fixed $B$. We also analyze the pairwise entanglement between nearest neighbors in three qubits. The pairwise entanglement, for a fixed $T$, can be strong by controlling $B$ and $J_z$. PACS: 03.65. Ud, 03.67…
We study the entanglement of a two-qubit one dimensional XYZ Heisenberg chain in thermal equilibrium at temperature T. We obtain an analytical expression for the entanglement of formation for this system in terms of the parameters of the Hamiltonian and T. We show that depending on the relation among the coupling constants it is possible to increase the amount of entanglement of the system increasing its anisotropy. We also show numerically that for all sets of the coupling constants entanglement is a monotonically decreasing function of the temperature T, proving that we must have at least an…
Various thermal correlations as well as the effect of intrinsic decoherence on the correlations are studied in a two-qubit Heisenberg XYZ spin chain with the Dzyaloshinski--Moriya (DM) interaction along the z direction, i.e. Dz. It is found that tunable parameter Dz may play a constructive role on the concurrence (C), classical correlation (CC) and quantum discord (QD) in thermal equilibrium while it plays a destructive role on the correlations in the intrinsic decoherence case. The entanglement and quantum discord exhibit collapse and revival under the phase decoherence. With a proper combina…
The entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence is studied. The usefulness of such system for performance of the quantum teleportation protocol ${\cal T}_0$ and entanglement teleportation protocol ${\cal T}_1$ is also investigated. The results depend on the initial conditions and the parameters of the system. For the product and maximally entangled initial states, increasing the size of spin-orbit interaction parameter $D$ amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of telep…
We examine the existence of completely separable ground states (GS) in finite spin-$s$ arrays with anisotropic $XYZ$ couplings, immersed in a non-uniform magnetic field along one of the principal axes. The general conditions for their existence are determined. The analytic expressions for the separability curve in field space, and for the ensuing factorized state and GS energy, are then derived for alternating solutions, valid for any spin and size. They generalize results for uniform fields and show that nonuniform fields can induce GS factorization also in systems which do not exhibit this p…
We investigate the characteristics of entanglement teleportation of a two-qubit Heisenberg XYZ model under different Dzyaloshinskii-Moriya interaction with intrinsic decoherence taken into account. The comparison of the two different Dzyaloshinskii-Moriya interaction, the effects of the initial state and the inputting state on the entanglement teleportation are presented. The results reveal that the dynamics of entanglement is a symmetry function about for the system, whereas it is not for the system. The ferromagnetic case is superior to the antiferromagnetic case for restrain decoherence whe…
Two qubit density matrices, which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initi…
The thermal entanglement of a two-qubit anisotropic Heisenberg $XYZ$ chain under an inhomogeneous magnetic field b is studied. It is shown that when inhomogeneity is increased to certain value, the entanglement can exhibit a larger revival than that of less values of b. The property is both true for zero temperature and a finite temperature. The results also show that the entanglement and critical temperature can be increased by increasing inhomogeneous exteral magnetic field.
Effects of DM and KSEA interactions on entanglement, Fisher and Wigner-Yanase information correlations of two XYZ-Heisenberg-qubit states under a magnetic field
The role of spin-orbit interaction on the ground state and thermal entanglement of a Heisenberg XYZ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. For a certain value of spin-orbit parameter $D$, the ground state entanglement tends to vanish suddenly and when $D$ crosses its critical value $D_c$, the entanglement undergoes a revival. The maximum value of the entanglement occurs in the revival region. In finite temperatures there are revival regions in $D-T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases…
We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model with antiferromagnetic couplings. Moreover, the sign and relative strength of the couplings characterizing the model are shown to be experimentally tunable. We display the rich phase diagram in the one-dimensional case and discuss finite size effects relevant for trapped systems. Finally, experimental issues relat…
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.
We investigate the entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya(DM) interaction and inhomogeneous magnetic field. It is found that the control parameters ($D_{x}$, $B_{x}$ and $b_{x}$) are remarkably different with the common control parameters ($D_{z}$,$B_{z}$ and $b_{z}$) in the entanglement and the critical temperature, and these x-component parameters can increase the entanglement and the critical temperature more efficiently. Furthermore, we show the properties of these x-component parameters for the control of entanglement. In the ground state, i…
We study dynamical properties of dissipative XYZ Heisenberg lattices where anisotropic spin-spin coupling competes with local incoherent spin flip processes. In particular, we explore a region of the parameter space where dissipative magnetic phase transitions for the steady state have been recently predicted by mean-field theories and exact numerical methods. We investigate the asymptotic decay rate towards the steady state both in 1D (up to the thermodynamical limit) and in finite-size 2D lattices, showing that critical dynamics does not occur in 1D, but it can emerge in 2D. We also analyze …
In order to explore the effect of external temperature $T$ in quantum correlation we compute thermal entanglement and thermal discord analytically in the Heisenberg $X$ $Y$ $Z$ model with Dzyaloshinskii-Moriya Interaction term ${\bm D} \cdot \left( {\bm σ}_1 \times {\bm σ}_2 \right)$. For the case of thermal entanglement it is shown that quantum phase transition occurs at $T = T_c$ due to sudden death phenomenon. For antiferromagnetic case the critical temperature $T_c$ increases with increasing $|{\bm D}|$. For ferromagnetic case, however, $T_c$ exhibits different behavior in the regions $|{\…
Generation and robustness of non-local correlations induced by Heisenberg XYZ and intrinsic decoherence models: (x,y)-spin-orbit interactions and $x$- magnetic field
Correlation beyond entanglement is a subject of interest in quantum information. Here we have shown the existence of quantum correlation without entanglement in Heisenberg $XYZ$ spin model with external magnetic field, using different versions of measurement-induced nonlocality. However maximally entangled states are shown to possess maximum correlation.
We determine the conditions under which general dimer-type spin chains with $XYZ$ couplings of arbitrary range in a general transverse field will exhibit an exactly separable parity-breaking eigenstate. We also provide sufficient conditions which ensure that it will be a ground state. We then examine the exact side limits at separability of the entanglement between any two spins in a finite chain, showing that in the vicinity of separability, the system will loose all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and in…
In the present paper we study two qubit entanglement in the most general $XYZ$ Heisenberg magnetic chain with (non)homogeneous magnetic fields and the DM anisotropic antisymmetric exchange interaction, arising from the spin-orbit coupling . The model includes all known results as particular cases, for both antiferromagnetic and ferromagnetic $XX, XY, XXX, XXZ, XYZ$ chains. The concurrence of two qubit thermal entanglement and its dependence on anisotropic parameters, external magnetic field and temperature are studied in details. We found that in all cases, inclusion of the DM interaction, whi…
We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through $XYZ$ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the r…
We analyze exact ground state (GS) separability in general $N$ particle systems with two-site couplings. General necessary and sufficient conditions for full separability, in the form of one and two-site eigenvalue equations, are first derived. The formalism is then applied to a class of $SU(n)$-type interacting systems, where each constituent has access to $n$ local levels, and where the total number parity of each level is preserved. Explicit factorization conditions for parity-breaking GS's are obtained, which generalize those for $XYZ$ spin systems and correspond to a fundamental GS multil…
We propose a new approach called Ket-Bra Entangled State (KBES) Method for converting master equation into Schrödinger-like equation. With this method, we investigate decoherence process and entanglement dynamics induced by a $2$-qubit spin chain that each qubit coupled with reservoir. The spin chain is an anisotropy $XYZ$ Heisenberg model in the external magnetic field $B$, the corresponding master equation is solved concisely by KBES method; Furthermore, the effects of anisotropy, temperature, external field and initial state on concurrence dynamics is analyzed in detail for the case that in…
We investigate how the quantum correlations (quantum discord) of a two-qubit one dimensional XYZ Heisenberg chain in thermal equilibrium depends on the temperature (T) of the bath and also on an external magnetic field B. We show that the behavior of the thermal quantum discord (QD) differs in many unexpected ways from the thermal entanglement. For example, we show situations where QD increases with T when entanglement decreases, cases where QD increases with T even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite T. We also show that by properly…
The quantum coherence of the two-site XYZ model with Dzyaloshinsky-Moriya (DM) interactions in an external inhomogenous magnetic field is studied. The DM interaction, the magnetic field and the measurement basis can be along different directions, and we examine the quantum coherence at finite temperature. With respect to the spin-spin interaction parameter, we find that the quantum coherence decreases when the direction of measurement basis is the same as that of the spin-spin interaction. When the spin-lattice interaction is varied, the coherence always increases irrespective of the relation …
Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in compact form. The ground state has a very interesting property: all the pairs of spins are equally entangled with each other. Therefore it is possible to engineer long-range entanglement in experimentally realizable spin systems on the one hand and study more closely quantum phase transition in such systems on the other.
The anisotropic Heisenberg two-spin-1/2 model in an inhomogeneous magnetic field with both antisymmetric Dzyaloshinsky-Moriya and symmetric Kaplan-Shekhtman-Entin-Wohlman-Aharony cross interactions is considered at thermal equilibrium. Using a group-theoretical approach, we find fifteen spin Hamiltonians and as many corresponding Gibbs density matrices (quantum states) whose eigenvalues are expressed only through square radicals. We also found local unitary transformations that connect nine of this fifteen state collection, and one of them is the X quantum state. Since such quantum correlation…
The Schr{ö}dinger-Robertson inequality generally provides a stronger bound on the product of uncertainties for two noncommuting observables than the Heisenberg uncertainty relation, and as such, it can yield a stricter separability condition in conjunction with partial transposition. In this paper, using the Schr{ö}dinger-Robertson uncertainty relation, the separability condition previously derived from the su(2) and the su(1,1) algebra is made stricter and refined to a form invariant with respect to local phase shifts. Furthermore, a linear optical scheme is proposed to test this invariant se…
Quantum Steering vs Entanglement and Extracting Work in an Anisotropic Two-Qubit Heisenberg Model in Presence of External Magnetic Fields with DM and KSEA Interactions
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The correspondence between the classical and the quantum criterion of separability for the system is obtained in terms of these functions. Entanglement is generic and separability is special. Some applications are discussed in commonly occuring examples and possibly in exotic systems.
The entanglement in a general Heisenberg antiferromagnetic chain of arbitrary spin-$s$ is investigated. The entanglement is witnessed by the thermal energy which equals to the minimum energy of any separable state. There is a characteristic temperature below that an entangled thermal state exists. The characteristic temperature for thermal entanglement is increased with spin $s$. When the total number of lattice is increased, the characteristic temperature decreases and then approaches a constant. This effect shows that the thermal entanglement can be detected in a real solid state system of l…
We show that ultracold polar diatomic or linear molecules, oriented in an external electric field and mutually coupled by dipole-dipole interactions, can be used to realize the exact Heisenberg XYZ, XXZ and XY models without invoking any approximation. The two lowest lying excited pendular states coupled by microwave or radio-frequency fields are used to encode the pseudo-spin. We map out the general features of the models by evaluating the models' constants as functions of the molecular dipole moment, rotational constant, strength and direction of the external field as well as the distance be…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of inseparability with light are not uncommon, but such demonstrations in physically well-separated massive systems, such as distinct gases of atoms, are new and present significant challenges and opportunities. Rigorous theoretical criteria are needed for demonstrating that given data are sufficient to confirm entanglement. Such criteria for experimental data have…
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 s…
We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for $n$-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary $n$-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.
We study the all-to-all connected $XYZ$ (anisotropic-Heisenberg) spin model with local and collective dissipations, comparing the results of mean field theory with the solution of the Lindblad quantum evolution. Leveraging the permutational symmetry of the model [N. Shammah et al., Phys Rev. A 98, 063815 (2018)], we find exactly (up to numerical precision) the steady state up to $N=95$ spins. We characterize criticality, studying, as a function of the number of spins $N$, the spin structure factor, the magnetization, the Liouvillian gap and the Von Neumann entropy of the steady state. Exploiti…
We show that intrinsic fluctuations in system control parameters impose limits on the ability of two-qubit (exchange) Hamiltonians to generate entanglement starting from mixed initial states. We find three classes for Gaussian and Laplacian fluctuations. For the Ising and XYZ models there are qualitatively distinct sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the…
We consider a finite one-dimensional Heisenberg XYZ spin chain under the influence of dissipative Lindblad environment obeying the Born-Markovian constrain in presence of an external magnetic field. We apply both closed and open boundary conditions at zero and finite temperature. We present an exact numerical solution for the Lindblad master equation of the system in the Liouville space. we find that, in the free spin chain (in absence of any environment), the entanglement at all ranges evolve in time in a non-uniform oscillatory form that changes significantly depending on the initial state, …
In this work, we address the ground state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence s…
This article explores the concurrence, including entanglement, in a two-qubit Heisenberg XXX chain with Dzyaloshinskii-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. The concurrence expression was developed using the physical variables connected with the chosen system. Our results indicate that temperature, the spin coupling constant $J$, the x-components $D_x$, and $Γ_x$ may all play a role in determining the degree of intricacy between states. Additionally, these findings imply that the separability of states is possible for high-temperature domains or ferromagnetic chains. …
We investigate the time dynamics of quantum correlations of the anisotropic Heisenberg model in a time-dependent magnetic field, in one-dimensional, ladder, and two-dimensional lattices. We find that quantum correlation measures in the entanglement-separability paradigm are ergodic in these systems irrespective of system parameters. However, information-theoretic quantum correlation measures can also be nonergodic, and exhibit a transition from nonergodic to ergodic behavior with the change of interaction strength in the direction of the magnetic field. We also observe that the transition poin…
In the present paper an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii-Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give ph…
We study the dynamics of a two-qubit system coupled through time dependent anisotropic $XYZ$ Heisenberg interaction in presence of a time varying non-uniform external magnetic field. Exact results are presented for the time evolution of the system under certain integrability conditions. Furthermore, the corresponding entanglement of the system is studied for different values of the involved parameters. We found that the time evolution and different properties of entanglement such as amplitude, frequency and profile can be finely tuned by the interplay of the characteristics of the time-depende…
Two-qubit system is the foundation of constructing the universal quantum gate. We have studied the two-qubit Rabi model for the general case and its generalizations with dipole, XXX and XYZ Heisenberg qubit-qubit interactions, which are commonly used in quantum computation. Their solutions are presented analytically with eigenstates can be obtained in terms of extended coherent states or Fock states and applied to the construction of the ultrafast two-qubit quantum gate in circuit QED and quantum state storage and transfer. Some novel kinds of quasi-exact solutions are found for specific sets …
The concepts of separability, entanglement, spin-squeezing and Heisenberg limit are central in the theory of quantum enhanced metrology. In the current literature, these are well established only in the case of linear interferometers operating with input quantum states of a known fixed number of particles. This manuscript generalizes these concepts and extends the quantum phase estimation theory by taking into account classical and quantum fluctuations of the particle number. Our analysis concerns most of the current experiments on precision measurements where the number of particles is known …
We consider a finite two-dimensional Heisenberg triangular spin lattice at different degrees of anisotropy coupled to a dissipative Lindblad environment obeying the Born-Markovian constrain at finite temperature. We show how applying an inhomogeneous magnetic field to the system may significantly affect the entanglement distribution and properties among the spins in the asymptotic steady state of the system. Particularly, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustnes…
We analyze the entanglement of SU(2)-invariant density matrices of two spins $\vec S_{1}$, $\vec S_{2}$ using the Peres-Horodecki criterion. Such density matrices arise from thermal equilibrium states of isotropic spin systems. The partial transpose of such a state has the same multiplet structure and degeneracies as the original matrix with eigenvalue of largest multiplicity being non-negative. The case $S_{1}=S$, $S_{2}=1/2$ can be solved completely and is discussed in detail with respect to isotropic Heisenberg spin models. Moreover, in this case the Peres-Horodecki ciriterion turns out to …
