Dynamical behavior of quantum correlations between two qubits coupled to an external environment

We investigate the dynamics of quantum correlations of a two-qubit system coupled to an external environment. We have considered both cases: a spin environment and a bosonic environment. In all cases, we have chosen the Bell-diagonal state as the initial state and computed the evolution of quantum correlations in terms of entanglement, quantum discord and trace distance geometric quantum discord. Special attention is paid to the singular quantum phenomena, such as entanglement sudden death, sudden transition and double sudden transitions from classical to quantum decoherence, which all depend on the initial state and the parameters related to the system and the environment. We find the trace distance geometric quantum discord has a good robustness in resisting the spin and bosonic environmental noise.     

Quantifying quantum correlations in fermionic systems using witness operators

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entanglement witness of a state with a class of problems known as semidefinite programs, which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robustness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann concurrence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.     

Generalized form of optimal teleportation witnesses

We propose a generalized form of optimal teleportation witness to demonstrate their importance in experimental detection of the larger set of entangled states useful for teleportation in higher dimensional systems. The interesting properties of our witness reveal that teleportation witness can be used to characterize mixed state entanglement using Schmidt numbers. Our results show that while every teleportation witness is also a entanglement witness, the converse is not true. Also, we show that a hermitian operator is a teleportation witness iff it is a decomposable entanglement witness. In addition, we analyze the practical significance of our study by decomposing our teleportation witness in terms of Pauli and Gell-Mann matrices, which are experimentally measurable quantities.     

A revisit to non-maximally entangled mixed states: teleportation witness,noisy channel and discord

We constructed a class of non-maximally entangled mixed states (Adhikari et al. in Quantum Inf Comput 10:0398, 2010) and extensively studied their entanglement properties and also their usefulness as teleportation channels. In this article, we have revisited our constructed state and have studied it from three different perspectives. Since every entangled state is associated with a witness operator, we have found a suitable entanglement as well as teleportation witness operator for our non-maximally entangled mixed states. We considered the noisy channel’s effects on our constructed states to see how much it affects the states’ capacities as teleportation channels. For this purpose, we have mainly focussed on amplitude damping channel. A comparative study on concurrence and quantum discord of our constructed state of Adhikari et al. (2010) has also been carried out here.     

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW??s are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance.     

Exploiting Kondo spin chains for generating long range distance independent entanglement

We investigate the entanglement properties of the Kondo spin chain when it is prepared in its ground state as well as its dynamics following a single bond quench. We show that a true measure of entanglement such as negativity enables to characterize the unique features of the gapless Kondo regime. We determine the spatial extent of the Kondo screening cloud and propose an ansatz for the ground state in the Kondo regime accessible to this spin chain; we also demonstrate that the impurity spin is indeed maximally entangled with the Kondo cloud. We exploit these features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce a fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain—even for very large chains—a constant high value independent of the length; in addition, it is thermally robust. Moreover, we show that high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.     

Asymptotic entanglement in quantum walks from delocalized initial states

We study the entanglement between the internal (spin) and external (position) degrees of freedom of the one-dimensional discrete time quantum walk starting from local and delocalized initial states whose time evolution is driven by Hadamard and Fourier coins. We obtain the dependence of the asymptotic entanglement with the initial dispersion of the state and establish a way to connect the asymptotic entanglement between local and delocalized states. We find out that the delocalization of the state increases the number of initial spin states which achieves maximal entanglement from two states (local) to a continuous set of spin states (delocalized) given by a simple relation between the angles of the initial spin state. We also carry out numerical simulations of the average entanglement along the time to confront with our analytical results.     

Robustness measure of hybrid intra-particle entanglement,discord, and classical correlation with initial Werner state

Quantum information processing is largely dependent on the robustness of non-classical correlations, such as entanglement and quantum discord. However, all the realistic quantum systems are thermodynamically open and lose their coherence with time through environmental interaction. The time evolution of quantum entanglement, discord, and the respective classical correlation for a single, spin-1/2 particle under spin and energy degrees of freedom, with an initial Werner state, has been investigated in the present study. The present intra-particle system is considered to be easier to produce than its inter-particle counterpart. Experimentally, this type of system may be realized in the well-known Penning trap. The most stable correlation was identified through maximization of a system-specific global objective function. Quantum discord was found to be the most stable, followed by the classical correlation. Moreover, all the correlations were observed to attain highest robustness under initial Bell state, with minimum possible dephasing and decoherence parameters.     

Multipartite entanglement in an XXZ spin chain with Dzyaloshinskii–Moriya interaction and quantum phase transition

We investigate the multipartite entanglement and trace distance of the one-dimensional anisotropic spin-1/2 XXZ spin chain with the Dzyaloshinskii–Moriya interaction and find that the Dzyaloshinskii–Moriya interaction can influence the entanglement distribution and increase the proportion of multipartite entanglement in the entanglement structure. Furthermore, we explore the quantum phase transition of the XXZ spin chain with Dzyaloshinskii–Moriya interaction by making use of the multipartite entanglement and trace distance along with the quantum renormalization group method. It is found that the first derivatives of renormalized multipartite entanglement and trace distance for the ground state have dramatic changes near the critical point, and the renormalized multipartite entanglement and trace distance obey the universal finite-size scaling laws in the vicinity of the quantum critical point.     

Quantifying entanglement of two relativistic particles using optimal entanglement witness

In a recent paper, it was shown that the projections of a relativistic spin operator (RSO) massive spin- \frac12{\frac{1}{2}} particle on a world-vector which can be in timelike or null tetrad direction are proportional to the helicity or Bargman-Wigner (BW) qubit, respectively. Here we consider Lorentz transformations of two-particle states, which have been constructed both in helicity basis. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p ₁ and p ₂) for each particle. Consequently, in 2D momentum subspace we describe the structure of one particle in terms of the four-qubit system. We present a new approach to quantification of relativistic entanglement based on entanglement witness (EW), which is obtained by a new method of convex optimization. In addition, Lorentz invariance of entanglement using BW qubit is also studied.     

Exploring the renormalization of quantum discord and Bell non-locality in the one-dimensional transverse Ising model

In this paper, the effect of external magnet field g on the relationship among the quantum discord, Bell non-locality and quantum phase transition by employing quantum renormalization-group (QRG) method in the one-dimensional transverse Ising model is investigated. In our model, external magnet field g can influence the phase diagrams. The results have shown that both the two quantum correlation measures can develop two saturated values, which are associated with two distinct phases: long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing. Additionally, quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block, but for nearest-neighbor blocks in the long-ranged ordered Ising phase. However, the block–block correlation in the paramagnetic phase is not strong enough to violate the Bell–CHSH inequality as the size of system becomes large. Furthermore, when the system violates the CHSH inequality, i.e., satisfies quantum non-locality, it needs to be entangled. On the other way, if the system obeys the CHSH inequality, it may be entangled or not. To gain further insight, the non-analytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.     

On the connection between quantum nonlocality and phase sensitivity of two-mode entangled Fock state superpositions

In two-mode interferometry, for a given total photon number N, entangled Fock state superpositions of the form \((|N-m\rangle _a|m\rangle _b+\mathrm{e}^{i (N-2m)\phi }|m\rangle _a|N-m\rangle _b)/\sqrt{2}\) have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser–Horne–Shimony–Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the N00N state \((|N\rangle _a|0\rangle _b+\mathrm{e}^{i N\phi }|0\rangle _a|N\rangle _b)/\sqrt{2}\) and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser–Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states.     

Entanglement in dipolar coupling spin system in equilibrium state

We study the appearance of the entangled states in a one-dimensional finite chain of dipolar-coupling nuclear spins of 1/2 in the conditions of thermodynamic equilibrium. It is shown that entanglement is achieved by the application of a low external magnetic field in which the Zeeman interaction energy is the order of or even less than the dipolar interaction one. When these energies are equal, the critical temperature, i. e. the temperature of the entanglement appearance, coincides with the temperature at which the heat capacity of the spin chain achieves its maximum. The obtained relationship between the critical temperature and the magnetic field can be considered as an entanglement witness. The dependences of the heat capacity on temperature and magnetic field have different character for entangled and separable states and can be served for experimental detection of entangled states.     

Local cloning of multipartite entangled states

No cloning theorem is a very fundamental issue in quantum mechanics. But the issue is much more involved if we consider quantum state shared among two or more than two parties and allow only local operation and classical communication. In the context of the fact that no known bipartite entangled state can be cloned by local operation and classical communication (LOCC) without assistance of extra entangled state, the cloning of unknown orthogonal entangled state becomes meaningful when there is some supply of free entanglement. With restriction on supply of free entanglement, various cases have been studied. In this paper, we try to give an overview of the subject and results that have been obtained across the literature along with a new result on probabilistic LOCC cloning of four Bell states.     

Relations between quantum correlations,purity and teleportation fidelity for the two-qubit Heisenberg XYZ system

Quantifying and understanding quantum correlations may give a direct reply for many issues regarding the interesting behaviors of quantum system. To explore the quantum correlations in quantum teleportation, we have used a two-qubit Heisenberg XYZ system with spin–orbit interaction as a quantum channel to teleport an unknown state. By using different measures and standard teleportation protocols, we have derived the analytical expressions for quantum discord, entanglement of formation, purity, and maximal teleportation fidelity of the system. We compare their different characteristics and analyze the relationships between these quantities.     

A low complexity scheme for entanglement distributor buses

For technological purposes and theoretical curiosity, it is very interesting to have a building block that produces a considerable amount of entanglement between on-demand sites through a simple control of a few sites. Here, we consider permanently-coupled spin networks and study entanglement generation between qubit pairs to find low-complexity structures capable of generating considerable entanglement between various qubit pairs. We find that in axially symmetric networks the generated entanglement between some qubit pairs is rather larger than generic networks. We show that in uniformly-coupled spin rings each pair can be considerably entangled through controlling suitable vertices. To set the location of controlling-vertices, we observe that the symmetry has to be broken for a definite time. To achieve this, a magnetic flux can be applied to break symmetry via Aharonov-Bohm effect. Such a set up can serve as an efficient entanglement distributor bus in which each vertex-pair can be efficiently entangled through exciting only one fixed vertex and controlling the evolution time. The low-complexity of this scheme makes it attractive for use in nanoscale quantum information processors.     

Nuclear polarization and entanglement in spin systems

We investigated relationships between entanglement measures and the order parameter (nuclear polarization) in nuclear spin systems controlled by the nuclear magnetic resonance (NMR) technique. Since spin polarization can be easily manipulated by the NMR technique, experimentalists are presented with an opportunity to study the dynamic properties of entanglement, i.e., the creation and evolution of entangled states. Our approach may constitute the basis for researching the relations between the entanglement measures and measurable parameters of order in other quantum systems. An erratum to this article can be found at