We show that a special type of entangled states, cluster states, can be created with Heisenberg interactions and local rotations in 2d steps where d is the dimension of the lattice. We find that, by tuning the coupling strengths, anisotropic exchange interactions can also be employed to create cluster states. Finally, we propose electron spins in quantum dots as a possible realization of a one-way quantum computer based on cluster states.
In the last two decades, magnetic, thermodynamic properties and bipartite thermal entanglement in diamond spin clusters and chains have been studied. Such spin structures are presented in various compounds. The ions of $Cu^{2+}$ in the natural mineral azurite are arranged in a diamond spin chain. There are no studies of the entanglement behaviour during the quantum evolution of such systems. Herein, we consider the evolution of entanglement in the diamond spin-1/2 cluster. This cluster consists of two central spins described by the anisotropic Heisenberg model, which interact with two side spi…
The incipient quantum phase transitions of relevance to nonzero fluctuations and entanglement in Heisenberg clusters are studied in this paper by exploiting negativity as a measure in bipartite and frustrated spin-1 anisotropic Heisenberg clusters with bilinear-biquadratic exchange, single-ion anisotropy and magnetic field. Using the exact diagonalization technique, it is shown that quantum critical points signaled by qualitative changes in behavior of magnetization and particle number are ultimately related to microscopic entanglement and collective excitations. The plateaus and peaks in spin…
Thermal entanglement of a geometrically frustrated spin-1 Heisenberg diamond cluster is examined within the framework of the exact diagonalization method by computing the measure of entanglement negativity. The calculated exact analytical results are applied in order to obtain theoretical prediction of the robustness of bipartite thermal entanglement of the tetranuclear nickel complex [Ni4(CO3)2(aetpy)8](ClO4)4 (aetpy = 2-aminoethyl-pyridine) against rising temperature and magnetic field.
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 derive energy minima for biseparable states in three- and four-spin systems, with Heisenberg Hamiltonian and s <= 5/2. These provide lower bounds for tripartite and quadripartite entanglement in chains and rings with larger spin number N. We demonstrate that the ground state of an $N$-spin Heisenberg chain is $N$-partite entangled, and compute the energy gap with respect to biseparable states for N <= 8.
We propose a scheme for parameter estimation with cluster states. We find that phase estimation with cluster states under a many-body Hamiltonian and separable measurements leads to a precision at the Heisenberg limit. As noise models we study the dephasing, depolarizing, and pure damping channels. Decoherence reduces the sensitivity but our scheme remains superior over several reference schemes with states such as maximally entangled states and product states. For small cluster states and fixed evolution times it remains at the Heisenberg limit for approximately 2 times as many qubits than al…
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.
Magnetic and magnetocaloric properties of a spin-1 Heisenberg diamond cluster with two different coupling constants are investigated with the help of an exact diagonalization based on the Kambe's method, which employs a local conservation of composite spins formed by spin-1 entities located in opposite corners of a diamond spin cluster. It is shown that the spin-1 Heisenberg diamond cluster exhibits several intriguing quantum ground states, which are manifested in low-temperature magnetization curves as intermediate plateaus at 1/4, 1/2 and 3/4 of the saturation magnetization. Besides, the spi…
The dynamics of coherence in a two-qubit Heisenberg XXX model with magnetic field in the presence of the intrinsic decoherence is investigated. We discuss the influence of dipole parameter, spin distance, magnetic field and initial state parameter on coherence of the long time limit situation. Then, we discuss how decoherence changes with time with the initial state parameter and the decoherence parameter.
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…
An indirect measurement model is constructed for an approximately repeatable, precise position measuring apparatus that violates the assertion, sometimes called the Heisenberg uncertainty principle, that any position measuring apparatus with noise epsilon brings the momentum disturbance no less than hbar/2epsilon in any input state of the apparatus.
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…
We studied the trance distance, the Hellinger distance, and the Bures distance geometric quantum discords (GQDs) for a two-spin Heisenberg {\it XX} chain with the Dzyaloshinsky-Moriya (DM) interaction and the external magnetic fields. We found that considerable enhancement of the GQDs can be achieved by introducing the DM interaction, and their maxima were obtained in the limiting case $D\rightarrow \infty$. The external magnetic fields and the increase of the temperature can also enhance the GQDs to some extent for certain special cases.
In this article, we study the high order term of the fidelity of the Heisenberg chain with next-nearest-neighbor interaction and analyze its connection with quantum phase transition of Beresinskii-Kosterlitz-Thouless type happened in the system. We calculate the fidelity susceptibility of the system and find that although the phase transition point can't be well characterized by the fidelity susceptibility, it can be effectively picked out by the higher order of the ground-state fidelity for finite-size systems.
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 analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits. We calculated the errors caused by imperfect pulses which implement the quantum logic gates. It is numerically demonstrated that the probability error is proportional to $ε^4$, while the phase error is proportional to $ε$, where $ε$ is the characteristic deviation from the perfect pulse duration.
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 explore quantum phase transitions in the spin-1/2 $XX$ chain with three-spin interaction in terms of local quantum Fisher information and one-way quantum deficit, together with the demonstration of quantum fluctuations. Analytical results are derived and analyzed in detail.
The features of the concurrences of the nearest-neighbor and the next-nearest-neighbor sites for one-dimensional Heisenberg model with the next-nearest-neighbor interaction are studied both at the ground state and finite temperatures respectively. Both concurrences are found to exhibit different behaviors at the ground state, which is clarified from the point of view of the correlation function. The threshold temperature with respective to different number of sites and the thermal concurrences of the system up to 12 sites are studied numerically.
It has been pointed out that for some types of measurement the Heisenberg uncertainty relation seems to be violated. In order to save the situation a new uncertainty relation was proposed by Ozawa. Here we introduce revised definitions of error and disturbance taking into account the gain associated with generalized measurement interactions. With these new definitions, the validity of the Heisenberg inequality is recovered for continuous linear measurement interactions. We also examine the changes in distribution functions caused by the general measurement interaction and clarify the physical …
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 consider the two-step method [A. R. Kuzmak and V. M. Tkachuk, Phys. Lett. A 378 (2014) 1469] for preparation of an arbitrary quantum gate on two spins with anisotropic Heisenberg interaction. At the first step, the system evolves during some period of time. At the second step, we apply pulsed magnetic field individually to each spin. We obtain the conditions for realization of SWAP, iSWAP, $\sqrt{SWAP}$ and entangled gates. Finally, we consider the implementation of this method on the physical system of ultracold atoms in optical lattice.
Spin cat states are promising candidates for quantum-enhanced measurement. Here, we analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where the uncertainty is inversely proportional to the total particle number. In order to fully exploit their metrological ability, we propose to use the interaction-based readout for implementing phase estimation. It is demonstrated that the interaction-based readout enables spin cat states to saturate their ultimate precision bounds. The interaction-based readout comprises a one-axis twisting, two $\f…
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A 72, 012331 (2005)]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For gen…
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 corrections to the Heisenberg interaction between several lateral, single-electron quantum dots. We show, using exact diagonalization, that three-body chiral terms couple triangular configurations to external sources of flux rather strongly. The chiral corrections impact single qubit encodings utilizing loops of three or more Heisenberg coupled quantum dots.
In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum co…
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for …
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…
In this paper the the effect of Dzyaloshinskii-Moriya interaction and anisotropy on the Entanglement of Heisenberg chain has been studied. While the anisotropy suppress the entanglement due to favoring of the alignment of spins, the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations. Thermodynamic limit of the model and emerging of non-analytic behavior of the entanglement have also been probed. The singularities of the entanglement correspond to the critical boundary separating different phases of the model. The singularity of the entanglement derivative…
In this paper, we investigate the thermal entanglement and teleportation of a thermally mixed entangled via a two-qubit Heisenberg XXX chain with the x-component $D_x$ of the Dzyaloshinskii-Moriya interaction. Our findings suggest that temperature $T$, spin coupling constant J, and the x-components $D_x$ may influence entanglement of the output states and, consequently, the possibilities of teleportation protocols. Furthermore, these results indicate that the entanglement of the output states requires a low-temperature regime, weak Dzyaloshinskii-Moriya interaction, or an antiferromagnetic cha…
Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in compact form. The ground state has a very interesting property: all the pairs of spins are equally entangled with each other. Therefore it is possible to engineer long-range entanglement in experimentally realizable spin systems on the one hand and study more closely quantum phase transition in such systems on the other.
In this paper, we convert the lattice configurations into networks with different modes of links and consider models on networks with arbitrary numbers of interacting particle-pairs. We solve the Heisenberg model by revealing the relation between the Casimir operator of the unitary group and the conjugacy-class operator of the permutation group. We generalize the Heisenberg model by this relation and give a series of exactly solvable models. Moreover, by numerically calculating the eigenvalue of Heisenberg models and random walks on network with different numbers of links, we show that a syste…
Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Her…
We study the quantum brachistochrone evolution for a system of two spins-$\frac{1}{2}$ described by an anisotropic Heisenberg Hamiltonian without $zx$, $zy$ interacting couplings in magnetic field directed along the z-axis. This Hamiltonian realizes quantum evolution in two subspaces spanned by $\|\uparrow\uparrow\rangle$, $\|\downarrow\downarrow\rangle$ and $\|\uparrow\downarrow\rangle$, $\|\downarrow\uparrow\rangle$ separately and allows to consider the brachistochrone problem on each subspace separately. Using the evolution operator for this Hamiltonian we generate quantum gates, namely an …
