Tripartite thermal correlations in an inhomogeneous spin–star system

Abstract

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 analyze the dependence of such correlations on the homogeneity of the 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.

Measure of tripartite entanglement in bosonic and fermionic systems

“…Specifically, we have shown that a good entanglement measure satisfying the requirements of the theoretical criterion introduced in this paper can be obtained from the TPN recently used in the context of non identical particles [18,19]. Indeed, it constitutes a very practical tool to evaluate the amount of quantum correlations appearing in three-boson or -fermion mixture states of low-dimensional systems, that can be extracted and then placed in standard quantum registers without any violation of the local particle number superselection rule.…”

Competition of direct and indirect sources of thermal entanglement in a spin-star network

“…Wan-Li et al have studied the thermal entanglement in a spin-star network with three peripheral spins [29], evaluating pairwise entanglement between all possible couples of spins. In Refs [30] and [31] a similar system has been analyzed, singling out tripartite thermal correlations by exploiting the tripartite negativity [32] and a genuine tripartite entanglement witness introduced by Huber et al [33], respectively. By the way, it is worth mentioning that such two tools have produced extremely similar predictions concerning the tripartite thermal entanglement of the outer spins.…”

“…In this paper we consider a natural extension of the system analyzed in Refs. [30,31], which consisted of three peripheral spins interacting with a central one (we call it 'indirect' coupling). Here, we investigate a similar situation, but with the addition of another interaction between the peripheral spins ('direct' coupling).…”

An algebraic approach to the study of multipartite entanglement

“…However, this functional gives only a clue about the presence of entanglement in mixed states, indeed in this case the condition given is neither necessary nor sufficient. Nevertheless, its effectiveness has been shown in the study of simple physical systems [11]. Another interesting quantity, introduced for detecting entanglement of pure states of three qubits, is the three-tangle [12], which is based on the concurrence and whose validity has been criticized [13].…”