Tripartite Negativity Research Articles

Tripartite entanglement of electron spins of noninteracting electron gases

By using the tripartite negativity as entanglement measure, we study the tripartite entanglement of electron spins of noninteracting electron gases. Our results imply that the tripartite entanglement depends on the relative distance between the three spins and the temperature. By a comparison between the tripartite negativity and quantum mutual information, for the symmetrical configuration that the relative distances between each pair of the three spins are the same, the quantum mutual information lasts a longer relative distance than the tripartite negativity does. While for the unsymmetrical configuration, the analysis imply that the tripartite negativity just measures the tripartite correlation while the quantum mutual information maybe takes the bipartite correlation into account.

Disentanglement, Bell-nonlocality violation and teleportation capacity of the decaying tripartite states

Dynamics of disentanglement as measured by the tripartite negativity and Bell nonlocality as measured by the extent of violation of the multipartite Bell-type inequalities are investigated in this work. It is shown definitively that for the initial three-qubit Greenberger–Horne–Zeilinger (GHZ) or W class state preparation, the Bell nonlocality suffers sudden death under the influence of thermal reservoirs. Moreover, all the Bell-nonlocal states are useful for nonclassical teleportation, while there are entangled states that do not violate any Bell-type inequalities, but still yield nonclassical teleportation fidelity.

Tripartite entanglement of a spin star model with Dzialoshinski–Moriya interaction

The effect of Dzialoshinski---Moriya (DM) interaction on the tripartite thermal entanglement of a spin-star model with four spins has been analyzed by an entanglement measure of the tripartite negativity. Our results imply that the tripartite thermal entanglement can be established among the three surrounding parties which do not interact with each other but interact with the central party independently. From the results, we find that the strong DM interaction can enhance the tripartite thermal entanglement while the high temperature can shrink it. The effect of the inhomogeneous coupling on the tripartite thermal entanglement is also discussed.

Measure of tripartite entanglement in bosonic and fermionic systems

We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed three-boson or three-fermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible number of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuous-time quantum walks of identical particles (for both bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: The bosonic bunching results in a low number of quantum correlations while Fermi-Dirac statistics allows for higher values of the entanglement.

Genuine tripartite entanglement in a spin-star network at thermal equilibrium

In a recent paper [M. Huber {\it et al}, Phys. Rev. Lett. {\bf 104}, 210501 (2010)] new criteria to find out the presence of multipartite entanglement have been given. We exploit these tools in order to study thermal entanglement in a spin-star network made of three peripheral spins interacting with a central one. Genuine tripartite entanglement is found in a wide range of the relevant parameters. A comparison between predictions based on the new criteria and on the tripartite negativity is also given.

Tripartite thermal correlations in an inhomogeneous spin–star system

We exploit the tripartite negativity to study the thermal correlations in a tripartite system, that is, the three outer spins interacting with the central one in a spin–star system. We analyse the dependence of such correlations on the homogeneity of interactions, starting from the case where central–outer spin interactions are identical and then focusing on the case where the three coupling constants are different. We single out some important differences between the negativity and the concurrence.

Entanglement dynamics in three-qubitXstates

I explore the entanglement dynamics of a three qubit system in an initial X-state undergoing decoherence including the possible exhibition of entanglement sudden death (ESD). To quantify entanglement I utilize negativity measures and make use of appropriate entanglement witnesses. The negativity results are then extended to X-states with an arbitraty number of qubits. I also demonstrate non-standard behavior of the tri-partite negativity entanglement metric, its sudden appearance after some amount of decoherence followed quickly by its disappearance. Finally, I solve for a lower bound on the three qubit X-state concurrence, demonstrate when this bound goes to zero, and outline simplifcations for the calculation of higher order X-state concurrences.

Tripartite entanglement transfer from flying modes to localized qubits

We investigate the process of entanglement transfer from a three-mode quantized field to a system of three spatially separated qubits each one made of a two-level atom resonantly coupled to a cavity mode. The optimal conditions for entanglement transfer, evaluated by atomic tripartite negativity, are derived for radiation prepared in qubit-like and Gaussian entangled states in terms of field parameters, atom-cavity interaction time, cavity mirror losses, and atomic preparation. For qubit-like states we found that for negligible cavity losses some states may completely transfer their entanglement to the atoms and/or be exactly mapped to the atomic state, whereas for Gaussian states we found a range of field parameters to obtain a large entanglement transfer. The purity of the three-qubit states and the entanglement of two-qubit subsystems are also discussed in some details.

Tripartite entanglement witnesses and entanglement sudden death

I explore entanglement dynamics in a three qubit system comparing the ability of entanglement witnesses to detect tripartite entanglement to the phenomenon of entanglement sudden death (ESD). Using a system subject to dephasing I invoke entanglement witnesses to detect tripartite Greenberger-Horne-Zeilinger (GHZ)-type and $W$-type entanglement and compare the evolution of their detection capabilities with the evolution of the negativity, bipartite concurrence, and tripartite negativity. Interestingly, I find a state in which there is no concurrence or tripartite negativity but there is entanglement. Finally, I utilize a three qubit quantum error correction code to address how ESD affects the abilities of quantum error correction.