The pairwise entanglement and local polarization of the ground state are discussed by studying the Heisenberg XX model in finite qubit case. The results show that: the ground state is composed by the micro state with the minimal total spin 0 (for even qubit) or 1/2 (for odd qubit), local polarization (LP) has intimate relation with the probability of the micro state in the ground state, the stronger the LP the smaller the probability, the same LP corresponding to the same probability; the pairwise entanglement of the ground state is the biggest in all the eigenvectors. We find when the qubit is small, the degenerate of state will decrease the pairwise entanglement, there has great different between the odd and the even qubit chain; when the qubit number is big, the effect of qubit number to the pairwise entanglement will disappear, the limited value will be round about 0.3424.
Basing on the calculation of all the pairwise entanglement in the $n$ ($n \leq 6$)-qubit Heisenberg XX open chain with system impurity, we find an important result: pairwise entanglement can only be transferred through entangled pair. The non-nearest pairwise entanglement will has the possibility to exist as long as there has even number qubit in their middle. This point means that we can get longer distance entanglement in solid system.
The effects of multi-impurity on the entanglement of anisotropic Heisenberg ring XXZ under a homogeneous magnetic field have been studied. The impurities make the equal pairwise entanglement in a ring compete with each other so that the pairwise entanglement exhibits oscillation. If the impurities are of larger couplings, both the critical temperature and pairwise entanglement can be improved
Consider the dynamics of a two-qubit entangled system in the decoherence environment, we investigate the stability of pairwise entanglement under decoherence. We find that for different decoherence models, there exist some special class of entangled states of which the pairwise entanglement is the most stable. The lifetime of the entanglement in these states is larger than other states with the same initial entanglement. In addition, we also investigate the dynamics of pairwise entanglement in the ground state of spin models such as Heisenberg and XXY models.
Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classifcation scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.
We study thermal entanglement in some low-dimensional Heisenberg models. It is found that in each model there is a critical temperature above which thermal entanglement is absent.
We study entanglement in dimerized Heisenberg systems. In particular, we give exact results of ground-state pairwise entanglement for the four-qubit model by identifying a Z_2 symmetry. Although the entanglements cannot identify the critical point of the system, the mean entanglement of nearest-neighbor qubits really does, namely, it reaches a maximum at the critical point.
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 study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria.
Recently, entanglement teleportation has been investigated in Phys. Rev. Lett. 84, 4236 (2000). In this paper we study entanglement teleportation via two separate thermally entangled states of two-qubit Heisenberg XX chain. We established the condition under which the parameters of the model have to satisfy in order to teleport entanglement. The necessary minimum amount of thermal entanglement for some fixed strength of exchange coupling is a function of the magnetic field and temperature.
We investigate the entanglement between any two spins in a one dimensional Heisenberg chain as a function of temperature and the external magnetic field. We find that the entanglement in an antiferromagnetic chain can be increased by increasing the temperature or the external field. Increasing the field can also create entanglement between otherwise disentangled spins. This entanglement can be confirmed by testing Bell's inequalities involving any two spins in the solid.
Inspired by the discrete-variable pairwise entanglement, in this work, we in theory analyze the continuous-variable pairwise entanglement between microwave modes based on a hybrid optoelectromechanical system, where the multi-pair microwave superconducting circuits simutaneously interact with each other via a mechanical resonator, which forms a Fabry-Pérot cavity along with a standing mirror. With experimentally reachable parameter settings, wanted entanglement can be acheived when the pair number up to 10, and more is also available, which has the potential to be useful in quantum technologie…
We compute the asymptotic entanglement capacity of the Ising interaction ZZ, the anisotropic Heisenberg interaction XX + YY, and more generally, any two-qubit Hamiltonian with canonical form K = a XX + b YY. We also describe an entanglement assisted classical communication protocol using the Hamiltonian K with rate equal to the asymptotic entanglement capacity.
By using the concept of negativity, we investigate entanglement in (1/2,1) mixed-spin Heisenberg systems. We obtain the analytical results of entanglement in small isotropic Heisenberg clusters with only nearest-neighbor (NN) interactions up to four spins and in the four-spin Heisenberg model with both NN and next-nearest-neighbor (NNN) interactions. For more spins, we numerically study effects of temperature, magnetic fields, and NNN interactions on entanglement. We study in detail the threshold value of the temperature, after which the negativity vanishes.
We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations of the ground-state and the first-excited-state entanglements are out of phase or in phase.
Kempe-Invariant Ordering of Three-Qubit Pairwise Entanglement under Local Depolarization
School of Physics and Materials Engineering, Hefei Normal University（合肥师范学院物理与材料工程学院）；School of Physics, Anhui University（安徽大学物理学院）；Leibniz International Joint Research Center of Materials Sciences of Anhui Province, Anhui University（安徽大学安徽省材料科学国际联合研究中心）
The entanglement dynamics of spin chains is investigated using Heisenberg-XY spin Hamiltonian dynamics. The various measures of two-qubit entanglement are calculated analytically in the time-evolved state starting from initial states with no entanglement and exactly one pair of maximally-entangled qubits. The localizable entanglement between a pair of qubits at the end of chain captures the essential features of entanglement transport across the chain, and it displays the difference between an initial state with no entanglement and an initial state with one pair of maximally-entangled qubits.
This is a thesis submitted to university of Pune, India, for the Ph.D. degree. This work deals with entanglement production in two qubit, two qutrit and three qubit systems, entanglement in indistinguishable fermionic systems, quantum discord in a Heisenberg chain and geometric measure of quantum discord in an arbitrary state of a bipartite quantum system.
Based on the idea of measuring the factorizability of a given density matrix, we propose a pairwise analysis strategy for quantifying and understanding multipartite entanglement. The methodology proves very effective as it immediately guarantees, in addition to the usual entanglement properties, additivity and strong super additivity. We give a specific set of quantities that fulfill the protocol and which, according to our numerical calculations, make the entanglement measure an LOCC non-increasing function. The strategy allows a redefinition of the structural concept of global entanglement.
We solve the eigenvalue problem of the five-qubit anisotropic Heisenberg model, without use of Bethe's Ansatz, and give analytical results for entanglement and mixedness of two nearest-neighbor qubits. The entanglement takes its maximum at Delta= (Delta>1) for the case of zero (finite) temperature with Delta being the anisotropic parameter. In contrast, the mixedness takes its minimum at Delta=1 (Delta>1) for the case of zero (finite) temperature.
The effects of boundary impurities on the entanglement entropy in an antiferromagnetic Heisenberg opened spin-$1/2$ chain are investigated. The method of density-matrix renormalization-group is used to obtain the bipartite entanglement. The entropy increases when the length of the subsystem increases. It will approach to a constant when system length is very large. With the same impurity interaction, qutrit impurities of spin-$1$ can increase the entanglement entropy.
The entanglement properties in an antiferromagnetic dimerized Heisenberg spin-1/2 chain are investigated. The entanglement gap, which is the difference between the ground-state energy and the minimal energy that any separable state can attain, is calculated to detect the entanglement. It is found that the entanglement gap can be increased by varying the alternation parameter. Through thermal energy, the witness of the entanglement can determine a characteristic temperature below that an entangled state can be obtained. The entanglement detected by the energy can provide a lower bound for that …
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…
Information transmission of two qubits through two independent 1D Heisenberg chains as a quantum channel is analyzed. It is found that the entanglement of two spin-$\frac 12$ quantum systems is decreased during teleportation via the thermal mixed state in 1D Heisenberg chain. The entanglement teleportation will be realized if the minimal entanglement of the thermal mixed state is provided in such quantum channel. High average fidelity of teleportation with values larger than 2/3 is obtained when the temperature {\it T} is very low. The mutual information $\mathcal{I}$ of the quantum channel de…
We calculate the entanglement between two spins in the ferromagnetic Heisenberg chain at low temperatures, and show that when only the ground state and the one particle states are populated, the entanglement profile is a gaussian with a characteristic length depending on the temperature and the coupling between spins. The magnetic field only affects the amplitude of the profile and not its characteristic length.
The effects of initial conditions and system parameters on entanglement dynamics and asymptotic entanglement for a two-qubit anisotropic XY Heisenberg system in the presence of an inhomogeneous magnetic field and spin-orbit interaction are investigated. We suppose that each qubit interacts with a separate thermal reservoir which is held in its own temperature. The effects of the parameters of the system and environment like spin-orbit interaction and temperature difference of reservoirs are also discussed.
We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic $XXZ$ model, and the ferromagnetic $XXZ$ model with anisotropy parameter $Δ\ge 1$. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the magnetic field can induce entanglement in the antiferromagnetic $XXX$ model, but cann…
Most of the work involving entanglement measurement focuses on systems that can be modeled by two interacting qubits. This is due to the fact that there are few studies presenting entanglement analytical calculations in systems with spins $s > 1/2$. In this paper we present for the first time an analytical way of calculating thermal entanglement in a dimension $2\otimes3$ Heisenberg chain through the distance between states. We use the Hilbert-Schmidt norm to obtain entanglement. The result obtained can be used to calculate entanglement in chains with spin-$1/2$ coupling with spin-$1$, such as…
In this letter, we show that the measure of entanglement using the generalized Bell inequality and the distance between states coincide when we use the Hilbert-Schmidt norm. Our conclusions apply to the spin-1/2 Heisenberg chains with interaction between the first neighbors.
Thermally stable quantum states with multipartite entanglements led by frustration are found in the antiferromagnetic spin-1/2 Heisenberg hexagon. The model has been solved exactly to obtain all analytic expressions of eigenvalues and eigenfunctions. Detection and characterizations for various types of entanglements have been carried out in terms of concurrence and entanglement witnesses based on several thermodynamic observables. Variations of entanglement properties with respect to temperature and frustration are discussed. Even though the frustration opposes the bipartite entanglement, it f…
Thermal entanglement of a two-qubit Heisenberg chain in presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as quantum channel are investigated. It is found that the DM interaction can excite the entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of input one, its dependences on the temperature, DM interaction and spin coupling constant are given in detail. Entanglement teleportation will be better realized via antiferromagnetic spin cha…
In this paper we consider the generation of a three-qubit GHZ-like thermal state by applying the entanglement swapping scheme of Zukowski {\it et al.} [Ann. N. Y. Acad. Sci. {\bf 755}, 91 (1995)] to three pairs of two-qubit Heisenberg XY chains. The quality of the resulting three-qubit entanglement is studied by analyzing the teleportation fidelity, when it is used as a resource in the teleportation protocol of Karlsson {\it et al.}[Phys. Rev. A {\bf 58}, 4394 (1998)]. We show that even though thermal noise in the original two-qubit states is amplified by the entanglement swapping process, we …
For a 3-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modeling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanc…
The concurrence of two alternate qubits in a four-qubit Heisenberg XX chain is investigated when a uniform magnetic field B is included. It is found that there is no thermal entanglement between alternate qubits if B is close to zero. Magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic cases. Near zero temperature, the entanglement undergoes two sudden changes with increasing value of the magnetic field B. This is due to the changes in the ground state. This novel property may be used as quantum entanglement switch. The anisotropy in the s…
The concurrence, a quantitative measure of the entanglement between a pair of particles, is determined for the case where the pair is extracted from a symmetric state of N two-level systems. Examples are given for both pure and mixed states of the N-particle system, and for a pair extracted from two ensembles with correlated collective spins.
The time evolution of the entanglement of a pair of two spin qubits is investigated when the two qubits simultaneously couple to an environment of an anisotropic Heisenberg XXZ spin chain. The entanglement of the two spin qubits can be created and is a periodic function of the time if the magnetic field is greater than a critical value. If the two spin qubits are in the Bell state, the entanglement can be stored with relatively large value even when the magnetic field is large.
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…
The thermal entanglement is investigated in a two-qubit Heisenberg XXZ system with Dzyaloshinskii-Moriya (DM) interaction. It is shown that the entanglement can be efficiently controlled by the DM interaction parameter and coupling coefficient $J_{z}$. $D_{x}$(the x-component parameter of the DM interaction) has a more remarkable influence on the entanglement and the critical temperature than $D_{z}$(the z-component parameter of the DM interaction). Thus, by the change of DM interaction direction, we can get a more efficient control parameter to increase the entanglement and the critical tempe…
The thermal entanglement in a two-qubit Heisenberg \emph{XXZ} spin chain is investigated under an inhomogeneous magnetic field \emph{b}. We show that the ground-state entanglement is independent of the interaction of \emph{z}-component $J_{z}$. The thermal entanglement at the fixed temperature can be enhanced when $J_{z}$ increases. We strictly show that for any temperature \emph{T} and $J_{z}$ the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field $b_{c}$ is independent of $J_{z}$. The critical magnetic field $B_{c}$ incr…
By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.
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.
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 explore the intimate relationship between quantum lithography, Heisenberg-limited parameter estimation and the rate of dynamical evolution of quantum states. We show how both the enhanced accuracy in measurements and the increased resolution in quantum lithography follow from the use of entanglement. Mathematically, the hyperresolution of quantum lithography appears naturally in the derivation of Heisenberg-limited parameter estimation. We also review recent experiments offering a proof of principle of quantum lithography, and we address the question of state preparation and the fabrication…
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 ex…
Using the adaptive time-dependent density-matrix renormalization group method, the dynamics of entanglement and quantum discord of a one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures. The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value. The quantum discord can be used to predict the quantum phase transition, while the entanglement cannot.
The long-range entanglement dynamics of an one-dimensional spin-1/2 anisotropic XXZ model are studied using the method of the adaptive time-dependent density-matrix renormalization-group. The long-range entanglement can be generated when a local quench on one of boundary bonds is performed in the system. The anisotropic interaction has a strong influence both on the maximal value of long-range entanglement and the time of reaching the maximum long-range entanglement. The local coupling has a notable impact on the long-range entanglement, but it can be neglected in the time of reaching the maxi…
Using an NMR quantum computer, we experimentally simulate the quantum phase transition of a Heisenberg spin chain. The Hamiltonian is generated by a multiple pulse sequence, the nuclear spin system is prepared in its (pseudo-pure) ground state and the effective Hamiltonian varied in such a way that the Heisenberg chain is taken from a product state to an entangled state and finally to a different product state.
The pairwise entanglement, measured by concurrence and geometric phase in $d=2,3$-dimensional free-fermion lattice systems have been studied for the ground state in this paper. Their derivation with respect to the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-fermion model that both concurrence and geometric phase shows the intimate connection with the correlation functions. The possible relation between concurrence and geometric phase has been also discussed…
We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits great…
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…
Thermal entanglement and teleportation properties in non-inertial frames are investigated when a two-qubit Heisenberg XXX model with Dzyaloshinski-Moriya (DM) interaction is used as the quantum channel. We find that thermal entanglement and the teleportation fidelity of a teleported state decrease with the acceleration parameter or temperature, in other words, the quantum entanglement teleportation will degenerate in non-inertial frames. Furthermore, our results also show that the average fidelity may be promoted by DM interaction for the ferromagnetic case, which is opposite to the antiferrom…
In previous work, we have developed a dynamic learning paradigm for "programming" a general quantum computer. A learning algorithm is used to find a set of parameters for a coupled qubit system such that the system at an initial time evolves to a state in which a given measurement results in the desired calculation value. This can be thought of as a quantum neural network (QNN). Here, we apply our method to a system of three qubits, and demonstrate training the quantum computer to estimate both pairwise and three-way entanglement.
A strongly coupled Heisenberg chain provides an important channel for quantum communication through its many-body ground state. Yet, the nature of the effective interactions and the ability to mediate long-range entanglement differs significantly for chains of opposite parity. Here, we contrast the characters of even and odd-size chains when they are coupled to external qubits. Additional parity effects emerge in both cases, depending on the positions of the attached qubits. Some striking results include (i) the emergence of maximal entanglement and (ii) Ruderman-Kittel-Kasuya-Yosida (RKKY) in…
The quantum entanglement dynamics of a one-dimensional spin-1/2 anisotropic XXZ model is studied using the method of the adaptive time-dependent density-matrix renormalization-group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of staggered magnetization quench are considered. The dynamics of pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two-spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a st…
We show that quantum entanglement and the Heisenberg uncertainty principle are inextricably connected. Toward this end, a complete set of commuting observables (CSCO) criterion for the entanglement is developed. Assuming (A1,A2,...) and (B1,B2,...) being two CSCO's for a given system, and C being the matrix, Cij = i [Bi,Aj], for each given row i (i=1,2,...) if at least one matrix element Cij (j=1,2,...) is nonzero, then for the simultaneous eigenstates |ψ)=|A1',A2',...) of (A1,A2,...), the simultaneous measurements of (B1,B2,...) are, in general,entangled. The only exception is when all the si…
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 study the threshold temperature for pairwise thermal entanglement in the spin-1/2 isotropic Heisenberg model up to 11 spins and find that the threshold temperature for odd and even number of qubits approaches the thermal dynamical limit from below and above, respectively. The threshold temperature in the thermodynamical limit is estimated. We investigate the many-particle entanglement in both ground states and thermal states of the system, and find that the thermal state in the four-qubit model is four-particle entangled before a threshold temperature.
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…
It has been shown that, for the two-qubit Heisenberg XY model, anisotropy and magnetic field may together be used to produce entanglement for any finite temperature by adjusting the external magnetic field beyond some finite critical strength. This interesting result arises from an analysis employing the Wootters concurrence, a computable measure of entanglement for two-qubit states. Recently, Mintert {\em et al.} proposed generalizations of Wootters concurrence for multipartite states. These MKB concurrences possess a mathematical property that enables one to understand the origin of this cha…
In the last two decades, magnetic, thermodynamic properties and bipartite thermal entanglement in diamond spin clusters and chains have been studied. Such spin structures are presented in various compounds. The ions of $Cu^{2+}$ in the natural mineral azurite are arranged in a diamond spin chain. There are no studies of the entanglement behaviour during the quantum evolution of such systems. Herein, we consider the evolution of entanglement in the diamond spin-1/2 cluster. This cluster consists of two central spins described by the anisotropic Heisenberg model, which interact with two side spi…
