We use the concept of negativity to study the entanglement of spin-1/2 and spin-5/2 antiferromagnetic Heisenberg model with an inhomogeneous magnetic field. Analytical conclusions of the model are acquired. It is found that the critical temperature $$T_\mathrm{c}$$Tc goes up, as the increase of anisotropy parameter $$k$$k. The temperature $$T_\mathrm{c}$$Tc becomes bigger than the results of spin-1/2 and spin-3/2 Heisenberg XXZ chain for the same value of $$k$$k. And we can gain more entanglement at higher temperature by coordinating the value of inhomogeneity $$b$$b.

We study the local thermal entanglement in a spin-1/2 Ising-XXZ diamond structure with two impurities. In this spin chain, we have two impurities with an isolated XXZ dimer between them. We focus on the study of the thermal entanglement in this dimer. The main goal of this paper is to provide a good understanding of the effect of impurities in the entanglement of the model. This model is exactly solved by a rigorous treatment based on the transfer-matrix method. Our results show that the entanglement can be tuned by varying the impurities parameters in this system. In addition, it is shown that the thermal entanglement for such a model exhibits a clear performance improvement when we control and manipulate the impurities compared to the original model without impurities. Finally, the impurities can be manipulated to locally control the thermal entanglement, unlike the original model where it is done globally.

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 concurrence of 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 by 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 external magnetic field in the z-direction to obtain a behavior where entanglement increases with T.

We studied the effects of inhomogeneous magnetic field on entanglement and teleportation in a two-qubit Heisenberg XXZ chain with intrinsic decoherence taken into account. The dependences of the entanglement and fully entangled fraction on the inhomogeneous magnetic fields b and time t are investigated in detail. The contrast between different initial states, including pure and mixed states, is presented.

We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions (QPT) that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a QPT.

We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional $\mathit{XYZ}$ Heisenberg chain in thermal equilibrium depend on the temperature $T$ of the bath and also on an external magnetic field $B$. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with $T$ when entanglement decreases, cases where QD increases with $T$ even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite $T$. We also show that by properly tuning $B$ or the interaction between the qubits we get nonzero QD for any $T$ and we present an effect not seen for entanglement, the ``regrowth'' of thermal QD.

We have studied the thermal entanglement as a function of the temperature for a two-qubits Heisenberg spins system; we have included Dzyaloshinskii–Moriya interaction (DM), an external magnetic field (EMF) and hyperfine interaction due to the nuclear field of the surrounding nuclei. A critical value for the EMF was found, around $$B^{(c)}_{\mathrm{ext},z} \sim 39$$Bext,z(c)∼39 mT, which characterizes two regimes of behavior of the thermal entanglement. Our results show that the DM term acts as a facilitator for the entanglement because it prolongs the nonzero thermal entanglement for larger temperatures. We found that the concurrence as a function of the temperature has a local maximum, for values of the magnetic field larger than the critical field. We also show that the critical temperature $$T_\mathrm{c}$$Tc follows a polynomial growth as a function of the DM term, with characteristic behavior $$T_{\mathrm{c}} \sim \beta _{0}^{2}$$Tc∼β02, and the hyperfine field implies a critical temperature as a function of the field variance, $$\sigma $$σ of the form $$T_{\mathrm{c}} \sim \sigma ^{2}$$Tc∼σ2. We show that in this system, the entanglement measure by the concurrence and the one-spin polarization observable exhibit opposite behavior, providing a method to obtain the entanglement from the measurement of an observable.

We formulate and discuss the explicit computation of dynamic correlation functions in open quadratic fermionic systems which are driven and dissipated by Lindblad jump processes that are linear in canonical fermionic operators. Dynamic correlators are interpreted in terms of a local quantum quench where the pre-quench state is a non-equilibrium steady state, i.e. a fixed point of the Liouvillian. As an example, we study the XY spin 1/2 chain and quadratic Majorana chains with boundary Lindblad driving, whose dynamics exhibit asymmetric (skewed) light cone behaviour. We also numerically treat the two-dimensional XY model and the XY spin chain with additional Dzyaloshinskii–Moriya interactions. The latter exhibits a new non-thermal phase transition which can be understood in terms of bifurcations of the quasi-particle dispersion relation. Finally, considering in some detail the periodic quadratic fermionic ring with dissipation at a single (arbitrary) site, we present analytical expressions for first order corrections (in the strength of dissipation) to the spectrum and non-equilibrium steady state (NESS) correlation functions.

We demonstrate that an arbitrary Bell state can be achieved in a two qubit anisotropic Heisenberg XY chain via Lyapunov control. During the whole process, we only need to apply an external field along a given direction to a single qubit. This control strategy is effective for all initial states in the four-dimensional Hilbert space where the target state is asymptotically stable. The effects of imperfections on the fidelity for the target state such as Gaussian leakage of local control and localized dephasing of individual spins are also considered.

We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.

Using Singh-Rajput MES as memory states in the evolutionary process of pattern storage and the non-evolutionary process of pattern recall (the two fundamental constituents of QuAM), the suitability and superiority of these MES over Bell’s MES have been demonstrated in both these processes. It has been shown that, under the operations of all the possible memorization operators for a two-qubit system, the first two states of Singh-Rajput MES are useful for storing the pattern |11> and the last two of these MES are useful in storing the pattern |10> while Bell’s MES are not much suitable as memory states in a valid memorization process. The recall operations have also been conducted by separately choosing Singh-Rajput MES and Bell’s MES as memory states for possible various queries and it has been shown that in each case the choices of Singh-Rajput MES as valid memory states are much more suitable than those of Bell’s MES.

This paper investigates the quantum dense coding of a three-qubit XXZ Heisenberg spin chain at thermal equilibrium, with three-site interactions in the presence of an external magnetic field. We analyze the effects of various system parameters on the dense coding in multiple cases with different types of three-site interactions. The results show that the most ideal case for dense coding is the model including both types of three-site interactions, with the imposed condition of XZX + YZY type of three-site interaction is larger than the XZY − YZX type of three-site interaction. The inclusion of the z direction coupling parameter JZ, and external magnetic parameter B are found to be effective for optimizing the dense coding capacity, while the temperature T is turned out to be destructive. Moreover, the ferromagnet (FM) is shown to be more ideal for quantum dense coding than the antiferromagnet (AFM). For FM, by comparing the two types of three-site interactions (XZY − YZX and XZX + YZY), the appropriate model for valid dense coding is suggested and their dominant regions are clarified.

The transitory and steady-state entanglement of a two-qubit XY Heisenberg magnetic spin system immersed in an external magnetic field are analyzed in terms of the entanglement measure of concurrence. The dependence of the system entanglement on coupling strength, decay rate, and applied magnetic field is numerically simulated for two distinct models of system evolution involving decoherence to the environment. An applied magnetic field was found to consistently reduce the system entropy. The external magnetic field increases entanglement for small strength, and if too strong, it reduces the entanglement. The maximum entanglement is formed from a balance of external magnetic field and the decay rate. The transitory level of entanglement in the system is found to oscillate with a frequency that is proportional to the magnetic field strength before reaching steady-state entanglement. It was found that collective decay produces more entanglement than individual decay.

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 a 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 threshold temperature can be increased by increasing inhomogeneous external magnetic field.

The quantum teleportation with the entangled thermal state is investigated based on the completely anisotropic Heisenberg chain in the presence of the externally inhomogeneous magnetic field. The effects of the anisotropy and magnetic field for the quantum fidelity are studied in detail. The zero temperature limit and the features of the nonzero temperature for this nonclassical fidelity are obtained. We find that the quantum teleportation demands more stringent conditions than the thermal entanglement of the resource by investigating the threshold temperature of the thermal concurrence and the critical temperature of the maximal teleportation fidelity. The useful quantum teleportation should avoid the point of the phase transition of the system and the anisotropy of the chain and the external magnetic field can control the applicability of the resource in the quantum teleportation.

The quantum Fisher information matrix provides us with a tool to determine the precision, in any multiparametric estimation protocol, through quantum Cramér–Rao bound. In this work, we study simultaneous and individual estimation strategies using the density matrix vectorization method. Two special Heisenberg XY models are considered. The first one concerns the anisotropic XY model in which the temperature T and the anisotropic parameter $$\gamma $$γ are estimated. The second situation concerns the isotropic XY model submitted to an external magnetic field B in which the temperature and the magnetic field are estimated. Our results show that the simultaneous strategy of multiple parameters is always advantageous and can provide a better precision than the individual strategy in the multiparameter estimation procedures.

The present work is devoted to studying the entanglement dynamics of two central spins coupled in a spin environment and subjected, simultaneously, to an external magnetic field changing with time t as an exponential function $${\mathfrak {B}}\left( 1-\mathrm{e}^{-\lambda t}\right) $$ . We want to determine whether interaction among central spins with an external magnetic field as well as preparation of bath in an appropriate spin coherent state, $$|\beta \rangle _\mathrm{{bath}}$$ , is shown to affect the decoherence process in a qualitatively significant manner. We show that the dynamics of the entanglement depends on the initial state of the central spins as well as the bath, the coupling constants and the strength of a magnetic field, $${\mathfrak {B}}, \lambda $$ . Compared with some cases already discussed in the literature as magnetic fields of periodic $$\sin (\lambda t)$$ and $$\cos (\lambda t)$$ functions, we can see that a magnetic field of exponential function $$\mathrm{e}^{-\lambda t}$$ plays a very crucial role in the entanglement generation between the two-spin qubits and its protection. To do this, we use an operator technique of the Holstein–Primakoff transformation, and the dynamics of the reduced density matrix of two coupled spin qubits is obtained in both finite and infinite numbers of bath spins. We also derive the concurrence measure to quantify the entanglement of the reduced density matrix of the two coupled central spins and look for conditions that provide information on whether this becomes robust against decoherence. It has been shown that the entanglement distribution can be both amplified, stabilized and protected with $${\mathfrak {B}}, \lambda $$ and $$\beta $$ . These results motivate developments toward the implementation or simulation of the purely theoretical model employing exponential fields.

Recently, Mazhar Ali (Phys. Rev. A, 81 (2010) 042303 and J. Phys. B, 43 (2010) 045504) showed the phenomenon of distillability sudden death (DSD) in qutrit-qutrit systems under amplitude damping. In this paper, the phenomenon of distillability sudden death in two-qutrit systems which are in the presence of the external magnetic field and Dzyaloshinskii-Moriya (DM) interaction under decoherence has been investigated. With the help of the realignment criterion, we show that certain initial prepared free entangled states may become bound entangled states in a finite time. Moreover, the effects of the external magnetic field strength and the DM interaction parameter, as well as the intrinsic decoherence parameter on the possibility of DSD in our model have been studied in detail.

Quantum phase transition in dimerised antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical (or critical like) points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs too in the same dimer chain. Though closed dimerised isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.

Making use of the master equation and effective Hamiltonian approach, we investigate the steady state entanglement in a three-qubit XX model. Both symmetric and nonsymmetric qubit-qubit couplings are considered. The system (the three qubits) is coupled to two bosonic baths at different temperatures. We calculate the steady state by the effective Hamiltonian approach and discuss the dependence of the steady state entanglement on the temperatures and couplings. The results show that for symmetric qubit-qubit couplings, the entanglements between the nearest neighbor are equal, independent of the temperatures of the two baths. The maximum of the entanglement arrives at TL = TR. For nonsymmetric qubit-qubit couplings, however, the situation is totally different. The baths at different temperatures would benefit the entanglement and the entanglements between the nearest neighbors are no longer equal. By examining the probability distribution of each eigenstate in the steady state, we present an explanation for these observations. These results suggest that the steady entanglement can be controlled by the temperature of the two baths.