In the present paper an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii-Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T=0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement.
Quantum entanglement is the quantum information processing resource. Thus it is of importance to understand how much of entanglement particular quantum states have, and what kinds of laws entanglement and also transformation between entanglement states subject to. Therefore, it is essentialy important to use proper measures of entanglement which have nice properties. One of the major candidates of such measures is "entanglement of formation", and whether this measurement is additive or not is an important open problem. We aim at certain states so-called "antisymmetric states" for which the add…
We study various distance-like entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be …
This report gives a lower bound of entanglement cost for antisymmetric states of bipartite d-level systems to be log_2 (d/(d-1)) ebit (for d=3, E_c >= 0.585...). The paper quant-ph/0112131 claims that the value is equal to one ebit for d=3, since all of the eigenvalues of reduced matrix of any pure states living in N times tensor product of antisymmetric space is not greater than 2^(-N) thus the von Neumann entropy is not less than N, but the proof is not true. Hence whether the value is equal to or less than one ebit is not clear at this moment.
In the present paper we study two qubit entanglement in the most general $XYZ$ Heisenberg magnetic chain with (non)homogeneous magnetic fields and the DM anisotropic antisymmetric exchange interaction, arising from the spin-orbit coupling . The model includes all known results as particular cases, for both antiferromagnetic and ferromagnetic $XX, XY, XXX, XXZ, XYZ$ chains. The concurrence of two qubit thermal entanglement and its dependence on anisotropic parameters, external magnetic field and temperature are studied in details. We found that in all cases, inclusion of the DM interaction, whi…
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 the entanglement cost of the states in the contragredient space, which consists of $(d-1)$ $d$-dimensional systems. The cost is always $\log_2 (d-1)$ ebits when the state is divided into bipartite $\C^d \otimes (\C^d)^{d-2}$. Combined with the arguments in \cite{Matsumoto02}, additivity of channel capacity of some quantum channels is also shown.
Mutual information and swap operation in the two-qubit Heisenberg model with the Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction are investigated. It is found that the mutual information I of such a quantum channel is sensitive to the initial conditions and declines with the increase of the temperature. The DM interaction can lead to a higher mutual information, especially for the ferromagnetic case. The entanglement quality of input states cannot enhance the mutual information of the quantum channel. When the DM interaction is large, the mutual information will be the maximum…
We analyse the entanglement of the antisymmetric state in dimension d x d and present two main results. First, we show that the amount of secrecy that can be extracted from the state is low, more precisely, the distillable key is bounded by O(1/d). Second, we show that the state is highly entangled in the sense that a large number of ebits are needed in order to create the state: entanglement cost is larger than a constant, independent of d. The second result is shown to imply that the regularised relative entropy with respect to separable states is also lower bounded by a constant. Finally, w…
The quantum renormalization group method is applied to study the quantum criticality and entanglement entropy of the ground state of the Ising chain in the presence of antisymmetric anisotropic couplings and alternating exchange interactions. The quantum phase transitions can be characterized by the discontinuity in the second derivative of the energy of renormalized ground state. The phase diagram is obtained by the critical boundary line. The first derivative of entanglement entropy also diverges at the same critical points after enough iterations of the renormalization of coupling constants…
We construct an entangled quantum heat engine (EQHE) based on two two-spin systems with Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction. By applying the explanations of heat transferred and work performed at the quantum level in Kieu's work [PRL, 93, 140403 (2004)], the basic thermodynamic quantities, i.e., heat transferred, net work done in a cycle and efficiency of EQHE are investigated in terms of DM interaction and concurrence. The validity of the second law of thermodynamics is confirmed in the entangled system. It is found that there is a same efficiency for both antiferr…
Entanglement is a powerful resource for processing quantum information. In this context pure, maximally entangled states have received considerable attention. In the case of bipartite qubit-systems the four orthonormal Bell-states are of this type. One of these Bell states, the singlet Bell-state, has the additional property of being antisymmetric with respect to particle exchange. In this contribution we discuss possible generalizations of this antisymmetric Bell-state to cases with more than two particles and with single-particle Hilbert spaces involving more than two dimensions. We review b…
We have synthesized the anti-symmetric spin exchange interaction (ASI), which is also called the Dzyaloshinskii-Moriya interaction, in a superconducting circuit containing five superconducting qubits connected to a bus resonator, by periodically modulating the transition frequencies of the qubits with different modulation phases. This allows us to show the chiral spin dynamics in three-, four- and five-spin clusters. We also demonstrate a three-spin chiral logic gate and entangle up to five qubits in Greenberger-Horne-Zeilinger states. Our results pave the way for quantum simulation of magneti…
We investigate the role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms. We calculate and illustrate graphically populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions. Our calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a tr…
We investigate effects of staggered magnetic field on thermal entanglement in the anisotropic XY model. The analytic results of entanglement for the two-site cases are obtained. For the general case of even sites, we show that when the anisotropic parameter is zero, the entanglement in the XY model with a staggered magnetic field is the same as that with a uniform magnetic field.
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 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 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 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.
We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two…
The photon-pairs generated through spontaneous parametric down-conversion (SPDC) possess strong correlations in their transverse position and momentum degrees of freedom. For such photon pairs, the transverse position correlation length depends on the crystal thickness and the pump wavelength, whereas the transverse momentum correlation length depends on the beam waist and spatial coherence length of the pump. By controlling these parameters, it is possible to engineer the spatial entanglement. Here, we utilize the circular asymmetry of the pump by using an elliptical-Gaussian beam to change t…
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.
A theoretical scheme to preserve the entanglement in a two-qubit-spin coupled system in the presence of Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction is proposed. Based on a sequence of operations performed periodically on the system, the scheme can preserve the entanglement of the system starting from any initial state with any high precision for any long duration.
We study the additivity property of three multipartite entanglement measures, i.e. the geometric measure of entanglement (GM), the relative entropy of entanglement and the logarithmic global robustness. First, we show the additivity of GM of multipartite states with real and non-negative entries in the computational basis. Many states of experimental and theoretical interests have this property, e.g. Bell diagonal states, maximally correlated generalized Bell diagonal states, generalized Dicke states, the Smolin state, and the generalization of Dür's multipartite bound entangled states. We als…
We investigate the intermediate permutational symmetries of a system of qubits, that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits picked at random with respect to the uniform measure on the unit sphere of the Hilbert space are almost as antisymmetric as they are allowed to be. We then observe that multipartite entanglement, measured by the generalized Meyer- Wallach measure, tends to be larger in subspaces that are more antisymmetric than the complete symmetric one. Eventually, we prove that all states contained in the most anti…
We show that the wave packet of a biphoton generated via spontaneous parametric down conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison of measurements performed in two different schemes: when the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected new results as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degr…
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 spin-orbit interaction in semiconductors is shown to result in an anisotropic contribution into the exchange Hamiltonian of a pair of localized conduction-band electrons. The anisotropic exchange interaction exists in semiconductor structures which are not symmetric with respect to spatial inversion, for instance in bulk zinc-blend semiconductors. The interaction has both symmetric and antisymmetric parts with respect to permutation of spin components. The antisymmetric (Dzyaloshinskii-Moriya) interaction is the strongest one. It contributes significantly into spin relaxation of localized …
Analytical expressions for the entanglement measures concurrence, i-concurrence and 3-tangle in terms of spin correlation functions are derived using general symmetries of the quantum spin system. These relations are exploited for the one-dimensional XXZ-model, in particular the concurrence and the critical temperature for disentanglement are calculated for finite systems with up to six qubits. A recent NMR quantum error correction experiment is analyzed within the framework of the proposed theoretical approach.
In this paper, we have given the symmetrical and antisymmetrical spin and space wave functions of three-electron, and further given the full total entanglement states for the three-electron, which are related to their space and spin wave function. When we study particles entanglement we not only consider their spin entanglement and also consider their space entanglement. Otherwise, we find that electrons entanglement are restricted to the teeny range, when electrons exceed the space range, their entanglement should be broken down even disappearance, which is accordance with the experiments res…
We analyze the effect of position dependent excitation phase on the properties of entanglement between two qubits formed in atomic systems. We show that the excitation phase induces a vacuum mediated quantum interference in the system that affects the dynamical behavior of entanglement between the qubits. It is also found that the quantum interference leads to a coherent population transfer between the symmetric and antisymmetric states which can considerably modify the dynamics of two-qubit entanglement and can even prevent finite time disentanglement (sudden death) under certain conditions.
We have applied our recent approach (Kargarian, et.al Phys. Rev. A 76, 60304 (R) (2007)) to study the quantum information properties of the anisotropic s=1/2 Heisenberg chain. We have investigated the underlying quantum information properties like the evolution of concurrence, entanglement entropy, nonanalytic behaviours and the scaling close to the quantum critical point of the model. Both the concurrence and the entanglement entropy develop two saturated values after enough iterations of the renormalization of coupling constants. This values are associated with the two different phases, i.e …
We study the thermal entanglement in the two-qubit anisotropic XXZ model and the Heisenberg model with Dzyaloshinski-Moriya (DM) interactions. The DM interaction is another kind of anisotropic antisymmetric exchange interaction. The effects of these two kinds of anisotropies on the thermal entanglement are studied in detail for both the antiferromagnetic and ferromagnetic cases.
We investigate the entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya(DM) interaction and inhomogeneous magnetic field. It is found that the control parameters ($D_{x}$, $B_{x}$ and $b_{x}$) are remarkably different with the common control parameters ($D_{z}$,$B_{z}$ and $b_{z}$) in the entanglement and the critical temperature, and these x-component parameters can increase the entanglement and the critical temperature more efficiently. Furthermore, we show the properties of these x-component parameters for the control of entanglement. In the ground state, i…
We analyze the role of resonances in two-fermion entanglement production for a quasi one-dimensional two channel scattering problem. We solve exactly for the problem of a two-fermion antisymmetric product state scattering off a double delta well potential. It is shown that the two-particle concurrence of the post-selected state has an oscillatory behavior where the concurrence vanishes at the values of momenta for virtual bound states in the double well. These concurrence zeros are interpreted in terms of the uncertainty in the knowledge of the state of the one particle subspace reduced one pa…
The thermal entanglement of a two-qubit anisotropic Heisenberg $XYZ$ chain under an inhomogeneous magnetic field b is studied. It is shown that when inhomogeneity is increased to certain value, the entanglement can exhibit a larger revival than that of less values of b. The property is both true for zero temperature and a finite temperature. The results also show that the entanglement and critical temperature can be increased by increasing inhomogeneous exteral magnetic field.
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…
The thermal quantum discord (QD) is studied in a two-qubit Heisenberg XXZ system with Dzyaloshinskii-Moriya (DM) interaction. We compare the thermal QD with thermal entanglement in this system and find remarkable differences between them. For instance, we show situations where QD decreases asymptotically to zero with temperature $T$ while entanglement decreases to zero at the point of critical temperature, situations where QD decreases with certain tunable parameters such as $D_z$ and $D_x$ when entanglement increases. We find that the characteristic of QD is exotic in this system and this pos…
The occupancies and entropic entanglement measures for the ground state of two particles in a two-dimensional harmonic anisotropic trap are studied. We implement a method to study the large interaction strength limit for different short- and long-range interaction potentials that allows to obtain the exact entanglement spectrum and several entropies. We show that for long-range interactions, the von Neumann, min-entropy and the family of Rényi entropies remain finite for the anisotropic traps and diverge logarithmically for the isotropic traps. In the short-range interaction case the entanglem…
The entanglement dynamics of a laser-pumped two-level quantum dot pair is investigated in the steady-state. The closely spaced two-level emitters, embedded in a semiconductor substrate, interact with both the environmental vacuum modes of the electromagnetic field reservoir as well as with the lattice vibrational phonon thermostat. We have found that the entanglement among the pair's components is substantially enhanced due to presence of the phonon subsystem. The reason is phonon induced decay among the symmetrical and antisymmetrical two-qubit collective states and, consequently, the populat…
Quantum Steering vs Entanglement and Extracting Work in an Anisotropic Two-Qubit Heisenberg Model in Presence of External Magnetic Fields with DM and KSEA Interactions
Entanglement is considered as a basic physical resource for modern quantum applications in Quantum Information and Quantum Computation theories. Interactions able to generate and sustain entanglement are subject to deep research in order to have understanding and control on it, based on specific physical systems. Atoms, ions or quantum dots are considered a key piece in quantum applications because is a basic piece of developments towards a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction which generates and modifies enta…
The concept of time delayed creation of entanglement by the dissipative process of spontaneous emission is investigated. A threshold effect for the creation of entanglement is found that the initially unentangled qubits can be entangled after a finite time despite the fact that the coherence between the qubits exists for all times. This delayed creation of entanglement, that we call sudden birth of entanglement, is opposite to the currently extensively discussed sudden death of entanglement and is characteristic for transient dynamics of one-photon entangled states of the system. We determine …
We study the effect of space anisotropy in the entanglement generated by expanding universe on spin 0 and 1/2 fields. For massive scalar field we find revivals of entanglement entropy vs momentum after decreasing from the maximum at k = 0. In massive Dirac field the effect is a slight distortion of the non-monotonic profile giving rise to the maximum of entanglement entropy at k > 0. More interestingly, massless field of both type can only get entangled through anisotropy, with a maximum of entanglement entropy occurring at k > 0.
"action at a distance" is a weird concept in quantum theory which people always avoid mentioning in most occasions. In this work, without involving any concept about "action at a distance", we naturally construct a physical structure that resembles quantum entanglement only based on the nonlocality of the wave function. To achieve this, we propose a nonlocal structure of the single particle wave function by means of a double-well potential model. In order to better describe this nonlocal system, we have also developed two kinds of representations: local representation and nonlocal representati…
Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions for the system are obtained after the model is re-expressed in terms of canonical variables, by performing a particular Bopp's shift to the noncommuting degrees of freedom. Employing Simon's separability criterion, we find that the states of the system are entangled provided a unique function of the (mass and frequency) parameters obeys an inequality. Entanglement of Formation for this system is also computed and its relation to the degree of anisotropy is discusse…
Atomic spectroscopy, an essential tool for frequency estimation, is widely used in quantum sensing. Atom-atom interaction can be used to generate entanglement for achieving quantum enhanced sensing. However, atom-atom interaction always induces collision shift, which brings systematic error in determining the resonance frequency. Contradiction between utilizing atom-atom interaction and suppressing collision shift generally exists in atomic spectroscopy. Here, we propose an antisymmetric Rabi spectroscopy protocol without collision shift in the presence of atom-atom interactions. We analytical…
In this work we find explicitly the decoherence free subspace (DFS) for a two two-level system in a common squeezed vacuum bath. We also find an orthogonal basis for the DFS composed of a symmetrical and an antisymmetrical (under particle permutation) entangled state. For any initial symmetrical state, the master equation has one stationary state which is the symmetrical entangled decoherence free state. In this way, one can generate entanglement via common squeezed bath of the two systems. If the initial state does not have a definite parity, the stationary state depends strongly on the initi…
A novel scheme is proposed for dissipative generation of maximally entanglement between two Rydberg atoms in the context of cavity QED. The spontaneous emission of atoms combined with quantum Zeno dynamics and Rydberg antiblockade guarantees a unique steady solution of the master equation of system, which just corresponds to the antisymmetric Bell state $|S\rangle$. The convergence rate is accelerated by the ground-state blockade mechanism of Rydberg atoms. Meanwhile the effect of cavity decay is suppressed by the Zeno requirement, leading to a steady-state fidelity about $90\%$ as the single-…
We demonstrate the irreversibility of asymptotic entanglement manipulation under quantum operations that completely preserve the positivity of partial transpose (PPT), resolving a major open problem in quantum information theory. Our key tool is a new efficiently computable additive lower bound for the asymptotic relative entropy of entanglement with respect to PPT states, which can be used to evaluate the entanglement cost under local operations and classical communication (LOCC). We find that for any rank-two mixed state supporting on the $3\otimes3$ antisymmetric subspace, the amount of dis…
Control of quantum entanglement has been considered as elemental physical resource for quantum applications in Quantum Information and Quantum Computation. Control of entangled states on a couple of atoms, ions or quantum dots are milestones in almost all quantum applications towards a scalable spin-based quantum computers or quantum devices. For magnetic systems, Ising model is an interaction which generates and modifies entanglement properties of quantum systems based on matter. In addition, when this interaction includes driven magnetic fields, it can be controlled to sustain, characterize …
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…
We investigate the entanglement properties of a one dimensional chain of spin qubits coupled via nearest neighbor interactions. The entanglement measure used is the n-concurrence, which is distinct from other measures on spin chains such as bipartite entanglement in that it can quantify "global" entanglement across the spin chain. Specifically, it computes the overlap of a quantum state with its time-reversed state. As such this measure is well suited to study ground states of spin chain Hamiltonians that are intrinsically time reversal symmetric. We study the robustness of n-concurrence of gr…
Using group-theoretical approach we found a family of four nine-parameter quantum states for the two-spin-1/2 Heisenberg system in an external magnetic field and with multiple components of Dzyaloshinsky-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. Exact analytical formulas are derived for the entanglement of formation for the quantum states found. The influence of DM and KSEA interactions on the behavior of entanglement and on the shape of disentangled region is studied. A connection between the two-qubit quantum states and the reduced density matrices of many-p…
We investigate the reduced dimensionality of highly anisotropic Bose-Einstein condensates (BECs) in connection to the entanglement between its spatial degrees of freedom. We argue that the reduced-dimensionality of the BEC is physically meaningful in a regime where spatial correlations are negligible. We handle the problem analytically within the mean-field approximation for general quasi-one-dimensional and -two-dimensional geometries, and obtain the optimal reduced-dimension, pure-state description of the condensate mean field. We give explicit solutions to the case of harmonic potentials, w…
We study optimal dense coding with thermal entangled states of a two-qubit anisotropic \emph{XXZ} model and a Heisenberg model with Dzyaloshinski-Moriya (DM) interactions. The DM interaction is another kind of anisotropic antisymmetric exchange interaction. The effects of these two kinds of anisotropies on dense coding are studied in detail for both the antiferromagnetic and ferromagnetic cases. For the two models, we give the conditions that the parameters of the models have to satisfy for a valid dense coding. We also found that even though there is entanglement, it is unavailable for our op…
