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 cannot induce entanglement in the ferromagnetic $XXX$ model.
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 the violations of Bell inequality for thermal states of qubits in a multi-qubit Heisenberg model as a function of temperature and external magnetic fields. Unlike the behaviors of the entanglement the violation can not be obtained by increasing the temperature or the magnetic field. The threshold temperatures of the violation are found be less than that of the entanglement. We also consider a realistic cavity-QED model which is a special case of the mutli-qubit Heisenberg model.
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.
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
We find that quantum teleportation, using the thermally entangled state of two-qubit Heisenberg XX chain as a resource, with fidelity better than any classical communication protocol is possible. However, a thermal state with a greater amount of thermal entanglement does not necessarily yield better fidelity. It depends on the amount of mixing between the separable state and maximally entangled state in the spectra of the two-qubit Heisenberg XX model.
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.
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.
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.
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…
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.
In this paper, we study the influence of anisotropy on the usefulness, of the entanglement in a two-qubit Heisenberg XY chain at thermal equilibrium in the presence of an external magnetic field, as resource for quantum teleportation via the standard teleportation protocol. We show that the nonzero thermal entanglement produced by adjusting the external magnetic field strength beyond some critical strength is a useful resource. We also considered entanglement teleportation via two two-qubit Heisenberg XY chains.
We consider quantum teleportation using the thermally entangled state of a three-qubit Heisenberg XX ring as a resource. Our investigation reveals interesting aspects of quantum entanglement not reflected by the pairwise thermal concurrence of the state. In particular, two mixtures of different pairs of W states, which result in the same concurrence, could yield very differrent average teleportation fidelities.
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…
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 …
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.
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…
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.
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…
We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.
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…
We study the two qubits Heisenberg XX chain with magnetic impurity in the presence of the external magnetic field and calculate the optimal fidelity of standard teleportation via the thermal equilibrium state. It is found that the combined influence of magnetic impurity and external magnetic field can increase the critical temperatures of entanglement and quantum teleportation without limit. The relation between two kinds of critical temperatures is revealed.
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.
In many-body quantum systems, the quantum Fisher information an observer can obtain is susceptible to decoherence. Consequently, quantum enhanced metrology, such as Heisenberg scaling, cannot usually be achieved. We show, via two distinct methods, that by applying periodic quantum error corrections, we can achieve the Heisenberg scaling for an extended period of time on a three-qubit Tavis-Cumming Model, where three two-level atoms interact with a single cavity mode, under certain approximations. The generalization to arbitrary number of atoms case is also discussed.
In this paper we study the swap operation in a two-qubit anisotropic XXZ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter within which the swap operation is feasible. The swap errors caused by the inhomogeneous field are evaluated.
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.
We describe an assembly of N superconducting qubits contained in a single-mode cavity. In the dispersive regime, the correlation between the cavity field and each qubit results in an effective interaction between qubits that can be used to dynamically generate maximally entangled states. With only collective manipulations, we show how to create maximally entangled quantum states and how to use these states to reach the Heisenberg limit in the determination of the qubit bias control parameter (gate charge for charge qubits, external magnetic flux for rf-SQUIDs).
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…
We investigate the teleportation of an entangled two-qubit state using three-qubit GHZ and W channels. The effects of white noise on the average teleportation fidelity and amount of entanglement transmitted are also studied.
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…
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…
We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system. We show that a player aware of the complex structure of the system used to implement the game can use this knowledge to gain higher mean payoff.
The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg--Langevin equation. Extension to the driven qubit fails---except for weak excitation---due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-…
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…
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 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…
In this Brief Report we show the relation between three-qubit entanglement invariants and two-qubit concurrence with the help of projective measurements. How to use these invariants to represent the entanglement property of three-qubit pure states is also investigated.
It is shown that the entanglement-structure of 3- and 4-qubit states can be characterized by optimized operators of the Mermin-Klyshko type. It is possible to discriminate between pure 2-qubit entanglements and higher entanglements. A comparison with a global entanglement measure and the i-concurrence is made.
