A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between majorization and renormalization group irreversibility emerges from our numerical analysis.
We study the entanglement properties of a closed chain of harmonic oscillators that are coupled via a translationally invariant Hamiltonian, where the coupling acts only on the position operators. We consider the ground state and thermal states of this system, which are Gaussian states. The entanglement properties of these states can be completely characterized analytically when one uses the logarithmic negativity as a measure of entanglement.
We investigate the possibility of chaining qubits by letting pairs of nearest neighbours qubits dissipating into common environments. We then study entanglement dynamics within the chain and show that steady state entanglement can be achieved.
We calculate exactly the entanglement content of magnon excited states in the integrable spin-1/2 XXX and XXZ chains in the scaling limit. In particular, we show that as far as the number of excited magnons with respect to the size of the system is small one can decompose the entanglement content, in the scaling limit, to the sum of the entanglement of particular excited states of free fermionic or bosonic theories. In addition we conjecture that the entanglement content of the generic translational invariant free fermionic and bosonic Hamiltonians can be also classified, in the scaling limit,…
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.
We discuss entanglement in the spin-1/2 anisotropic ferromagnetic Heisenberg chain in the presence of a boundary magnetic field generating domain walls. By increasing the magnetic field, the model undergoes a first-order quantum phase transition from a ferromagnetic to a kink-type phase, which is associated to a jump in the content of entanglement available in the system. Above the critical point, pairwise entanglement is shown to be non-vanishing and independent of the boundary magnetic field for large chains. Based on this result, we provide an analytical expression for the entanglement betw…
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 show how multi-partite entanglement, such as of W-state form, can be created in branched spin chain systems. We also discuss the preservation of such entanglement, once created. The technique could be applied to actual spin chain systems, or to other physical systems such as strings of coupled quantum dots, molecules or atoms.
A relation between entanglement and criticality of spin chains is established. The entanglement we exploit is shared between auxiliary particles, which are isolated from each other, but are coupled to the same critical spin-1/2 chain. We analytically evaluate the reduced density matrix, and numerically show the entanglement of the auxiliary particles in the proximity of the critical points of the spin chain. We find that the entanglement induced by the spin-chain may reach one, and it can signal very well the critical points of the chain. A physical understanding and experimental realization w…
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…
Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half chain. Our result is complementary to the known relation between non-translational invariant, nearest neighbor interacting Hamiltonians and QMA complete…
We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding mod…
For the XXZ chain, we discuss the relation between a lattice version of Unruh effect and the ground-state entanglement on the basis of the corner Hamiltonian. We find that the lattice Unruh temperature is interpreted as $β_λ= 2π/a$ with an effective acceleration $a=π/λ$, where $λ$ denotes the anisotropy parameter of the XXZ chain. Using quantum Monte Carlo simulation for the corner Hamiltonian at $β_λ$, we demonstrate that world lines of spins surrounding the entangle point provides an intuitive understanding the quantum entanglement. We also propose an XXZ-chain analogue of the detector for t…
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.
We study the dynamics of a single excitation in an infinite XXZ spin chain, which is launched from the origin. We study the time evolution of the spread of entanglement in the spin chain and obtain an expression for the second order spatial moment of concurrence, about the origin, for both ordered and disordered chains. In this way, we show that a finite central disordered region can lead to sustained superballistic growth in the second order spatial moment of entanglement within the chain.
We exploit the inherent entanglement of the ground state of a spin chain with dimerized XX or XXZ Hamiltonian to investigate the entanglement generation between the ends of the chain. We follow the strategy has been introduced in Ref. [14] to encode the information in the entangled ground state of the system by local rotation. The amount of achieved entanglement in this scheme is higher than the attaching a pair of maximally entanglement scenarios. Also, our proposal can be implemented by using the optical lattices.
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 …
In a ferromagnetic spin chain, the control of the local effective magnetic field allows to manipulate the static and dynamical properties of entanglement. In particular, the propagation of quantum correlations can be driven to a great extent so as to achieve an entanglement transfer on demand toward a selected site.
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 discuss the effect of a single diagonal defect on both the static and dynamical properties of entanglement in a spin chain. We show that entanglement localizes at the defect and discuss its localization length, arguing that this can be used as a mean to store entanglement. We also show that the impurity site can behave as an entanglement mirror and characterize the bouncing process in terms of reflection and transmission coefficients.
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…
We investigate entanglement in a linear chain of $N$ polar molecules coupled by dipole interaction. In our model, nearest neighbour interaction predominate, and we compute entanglement with the help of a two-party correlation entanglement measure. We find that, in this system, only excited states are entangled. Moreover, when an electrostatic field is applied, energy levels crossings occur, changing significantly the system's entanglement properties. We make a systematic study of the entanglement dependency on the inter molecular distance separating pairs of molecules, different partitions of …
The evolution of entanglement in a one-dimensional Ising chain is numerically studied under various initial conditions. We analyze two problems concerning the dynamics of the entanglement: (i) generation of the entanglement from the pseudopure separable state and (ii) transportation of the entanglement from one end of the chain to the other. The investigated model is a one-dimensional Ising spin-1/2 chain with nearest-neighbor interactions placed in an external magnetic field and irradiated by a weak resonant transverse field. The possibility of selective initialization of partially entangled …
We show how branching spin chains can be used to both generate and distribute entanglement from their natural dynamics. Such entanglement provides a useful resource, for example for teleportation or distributed quantum processing. Once distributed, this resource can be isolated through mapping or swapping the entanglement into specific qubits at the ends of branches. Alternatively, as we demonstrate for distributed bipartite entanglement, applying simple single-qubit operations to the end spin of one or more branches can dynamically freeze the entanglement at the branch ends.
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.
We derive temporally shaped control pulses for the creation of long-distance entanglement in disordered spin chains. Our approach is based on a time-dependent target functional and a time-local control strategy that permits to ensure that the description of the chain in terms of matrix product states is always valid. With this approach, we demonstrate that long-distance entanglement can be created even for substantially disordered interaction landscapes.
We examine the maximum entanglement reached by an initially fully aligned state evolving in an XY Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of [n/2] peaks in the global entanglement for an $n$-spin chain), whose width is proportional t…
We study the ground state as well as the dynamics of chains of bosons with local repulsive interactions and nearest-neighbour exchange using numerical techniques based on density matrix decimation. We explore the development of entanglement between the terminal sites of such chains as mechanisms are invoked to concentrate population in these sites. We find that long-range entanglement in the ground state emerges as a result of hopping taking place at the whole chain length in systems with appropriate hopping coefficients. Additionally, we find appropriate perturbations to increase the entangle…
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…
A formula to evaluate the entanglement in an one-dimensional ferrimagnetic system is derived. Based on the formula, we find that the thermal entanglement in a small size spin-1/2 and spin-s ferrimagnetic chain is rather robust against temperature, and the threshold temperature may be arbitrarily high when s is sufficiently large. This intriguing result answers unambiguously a fundamental question: ``can entanglement and quantum behavior in physical systems survive at arbitrary high temperatures?"
We propose to use ferromagnetic systems for entanglement generation and distribution together with perfect state transfer between distant parties in a qubit chain. The scheme relies on an effective 2-qubit dynamics, realized by leaving two empty sites in a uniformly filled chain. This allows long-range interacting qubit chains to serve as quantum channels for both tasks with optimal performances. Remarkably, the entanglement between sender and receiver sites is independent of both the transmission distance and of system size. This property opens new perspectives for short and mid-range quantum…
The limitations on the production and profitability of entanglement in a harmonic chain under strong driving are considered. We report on the limits of attainable entanglement for a given set of squeezings of the eigenmodes, showing that the higher the entanglement the more oscillatory and thus less easy to profit from. We also comment on propagation properties of entanglement, discussing the role of fast rotating terms and illustrating several issues with the example of a sudden switch of the coupling.
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.
The entanglement in a general mixed spin chain with arbitrary spin $S$ and 1/2 is investigated in the thermodynamical limit. The entanglement is witnessed by the magnetic susceptibility which decides a characteristic temperature for an entangled thermal state. The characteristic temperature is nearly proportional to the interaction $J$ and the mixed spin $S$. The bound of negativity is obtained on the basis of the magnetic susceptibility. It is found that the macroscopic magnetic properties are affected by the quantum entanglement in the real solids. Meanwhile, the entanglement can be quantita…
We investigate the presence of multipartite entanglement in macroscopic spin chains. We discuss the Heisenberg and the XY model and derive bounds on the internal energy for systems without multipartite entanglement. Based on this we show that in thermal equilibrium the above mentioned spin systems contain genuine multipartite entanglement, even at finite modest temperatures.
Entanglement entropy (EE) in critical quantum spin chains described by 1+1D conformal field theories contains signatures of the universal characteristics of the field theory. Boundaries and defects in the spin chain give rise to universal contributions in the EE. In this work, we analyze these universal contributions for the critical Ising and XXZ spin chains for different conformal boundary conditions and defects. For the spin chains with boundaries, we use the boundary states for the corresponding continuum theories to compute the subleading contribution to the EE analytically and provide su…
We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of multipartite entanglement.
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…
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.
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.
We study the scaling of the traces of the integer powers of the partially transposed reduced density matrix and of the entanglement negativity for two spin blocks as function of their length and separation in the critical Ising chain. For two adjacent blocks, we show that tensor network calculations agree with universal conformal field theory (CFT) predictions. In the case of two disjoint blocks the CFT predictions are recovered only after taking into account the finite size corrections induced by the finite length of the blocks.
We study the effect of a phase shift on the amount of transferrable two-spin entanglement in a spin chain. We consider a ferromagnetic Heisenberg/XY spin chain, both numerically and analytically, and two mechanisms to generate a phase shift, the Aharonov-Casher effect and the Dzyaloshinskii-Moriya interaction. In both cases, the maximum attainable entanglement is shown to be significantly enhanced, suggesting its potential usefulness in quantum information processing.
We study the ground-state entanglement of one-dimensional harmonic chains that are coupled to each other by a collective interaction as realized e.g. in an anisotropic ion crystal. Due to the collective type of coupling, where each chain interacts with every other one in the same way,the total system shows critical behavior in the direction orthogonal to the chains while the isolated harmonic chains can be gapped and non-critical. We derive lower and most importantly upper bounds for the entanglement,quantified by the von Neumann entropy, between a compact block of oscillators and its environm…
Since star network of spins was proposed, generating entanglement directly through spin interactions between distant parties became much possible. We propose an architecture which involves coupled spin chains based on nitrogen-vacancy centers and nitrogen defect spins to expand star network, the numerical analysis shows that the length of spin chains $M$ and spin noise can determine the maximally achievable entanglement $E_m$. The entanglement capability of this configuration under effect of disorder and spin loss is also studied. Moreover, it is shown that with this kind of architecture, star…
We investigate the entanglement properties of a finite size 1+1 dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.
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 study the possibility of using an uniformly coupled finite antiferromagnetic spin-1/2 Heisenberg chain as a channel for transmitting entanglement. One member of a pair of maximally entangled spins is initially appended to one end of a chain in its ground state and the dynamical propagation of this entanglement to the other end is calculated. We show that compared to the analogous scheme with a ferromagnetic chain in its ground state, here the entanglement is transmitted faster, with less decay, with a much higher purity and as a narrow pulse form rising non-analytically from zero. Here non-…
We consider the high probability state transfers and entanglements between different nodes of the spin-1/2 chains governed by the XXZ-Hamiltonian using the inhomogeneous stationary external magnetic field. Examples of three-, four-, ten- and twenty-node chains are represented. A variant of realization of the proper inhomogeneous magnetic field is discussed.
Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in t…
The entanglement-sharing properties of an infinite spin-chain are studied when the state of the chain is a pure, translation-invariant state with a matrix-product structure. We study the entanglement properties of such states by means of their finitely correlated structure. These states are recursively constructed by means of an auxiliary density matrix ρon a matrix algebra B and a completely positive map E: A \otimes B -> B, where A is the spin 2\times 2 matrix algebra. General structural results for the infinite chain are therefore obtained by explicit calculations in (finite) matrix algebra…
We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate CHSH inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. However, if this number is achieved then for some results of Bell measurements obtained in the protocol of entanglement swapping the output state violates CHSH inequality. Moreover, we show that for different states we have different critical numbers for which CHSH inequality is activated.
The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii--Moriya (DM) interaction considered as Gaussian distribution, the entanglement in one-dimensional random $XY$ spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entan…
Entanglement is believed to be crucial in macroscopic physical systems for understanding the collective quantum phenomena such as quantum phase transitions. We start from and solve exactly a novel Yang-Baxter spin-1/2 chain model with inhomogeneous and anisotropic short-range interactions. For the ground state, we show the behavior of neighboring entanglement in the parameter space and find that the inhomogeneous coupling strengths affect entanglement in a distinctive way from the homogeneous case, but this would not affect the coincidence between entanglement and quantum criticality.
Dynamics of the one-dimensional open Ising chain under influence of $π$ -pulses is studied. It is shown that the application of a specific sequence of such instant kicks to selective spins stimulates arising of perfect dynamical pairwise entanglement between ends of the spin chain. Analytic formulas for the concurrence dynamics are derived. It is also shown that the time required to perfectly entangle the ends of the chains grows linearly with the number of spins in the chain. The final entangled state of the ending spins is always the same and does not depend on length the chain.
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 …
The quantum entanglement is an important feature of many protocols in the field of quantum computing. In this paper we evaluate a level of entanglement in short qutrit chains. This evaluation is carried out with use of the CCNR criterion and the concurrence measure. We also present some explicit formulae describing the values of CCNR criterion and concurrence for exemplary short spin chains. Utilizing the obtained results, we indicate that analyzing the level of entanglement allows to detect the noise or deviation in the transfer process, in comparison to the perfect transfer where only operat…
he thermal entanglement is generated by weakly interacting atoms with an isotropic spin-1 chain. The decoherence of the entanglement is mainly investigated. The effective Hamiltonian is analytically obtained by the approximation method of perturbation. The scaling behavior of the effective coupling is numerically illustrated by the exact diagonalization. It is found out that the decay of the entanglement is slow in the case of non interacting spins. The long-distance thermal entangled states can be used as the noisy channel for the achievement of the quantum teleportation.
