Some entanglement features exhibited by two, three and four qubits interacting with an environment in a non-Markovian regime

Abstract

We explore various aspects of the quantum entanglement dynamics of systems of two, three and four qubits interacting with an environment at zero temperature in a non-Markovian regime, as described by the paradigmatic model recently studied by Bellomo, Lo Franco, and Compagno [Bellomo et al. Phys. Rev. Lett. 99 (2007) 160502]. We consider important families of initial states for the alluded systems. The average, typical entanglement evolution associated with each of these families is determined, and its relation with the evolution of the global degree of mixedness of the multi-qubit system is explored. For three and four qubits we consider the family of initial states equivalent under local unitary transformations to the |GHZ and |W states, and compare their average behavior with the average behavior exhibited by initial maximally entangled twoqubits states. Furthermore, in the case of two qubits, the evolution of other manifestations of entanglement, related to measurable quantities, is also investigated. In particular, we consider the Mintert-Buchleitner concurrence lower bound and an entanglement indicator based upon the violation of local uncertainty relations.

Typical Behavior of the Global Entanglement of an Open Multiqubit System in a Non-Markovian Regimen

“…It transpires from this figure that the finite time intervals of zero entanglement are longer in the case of six qubits than in the case of three qubits. This suggests that the lengths of these intervals tend to increase with the number of qubits, consistently with other results for particular states recently reported in [32]. This trend, however, is not observed when we evaluate the average entanglement evolution corresponding to random initial pure states, as can be appreciated in figure 2.b.…”

“…A particularly interesting feature of this process, first pointed out by Zyczkowski and the Horodeckis in a pioneering effort almost ten years ago [21], is that sometimes entanglement vanishes completely in a finite time. This remarkable phenomenon, known as entanglement sudden death (ESD), has been the subject of several theoretical and experimental studies [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

“…These works considered a system consisting of two independent qubits interacting with an environment at zero temperature in a non-Markovian regime. The entanglement dynamics of open multiqubit systems in non-Markovian regimes has also been considered in various recent works [29,30,32]. In particular, multiqubit systems evolving from initial GHZ or W states have been studied in detail in [29,30].…”

Dynamics of entanglement and state-space trajectories followed by a system of four-qubit in the presence of random telegraph noise: common environment (CE) versus independent environments (IEs)

“…However, the ultimate threat to the reliable practical implementation of quantum technologies base on creation and manipulation of multi-partite entangled states is the phenomenon of decoherence which is due to the unavoidable interaction of the quantum system with its external environment (open quantum system). In fact, such an interaction, independently to the quantum or classical nature of the external environment, is very fatal to the survival of the amount of quantum entanglement between the different constituent parts of a multi-partite quantum system [7,8]. More precisely, the phenomenon of decoherence results in the destruction of the typical quantum properties of the system, such as quantum entanglement and consequently, after a finite interaction time, the state of the system may in some cases undergoes a transition from an entangled to a separable state.…”

“…Nevertheless, many different entanglement measures for multi-partite entangled quantum systems defined as the sum of the bipartite entanglement measures over all the possible bi-partitions of total quantum system have been proposed during the years [40,41] (see also the review papers [42,43] and the references therein) and some interesting results based on this strategy have been obtained [44][45][46][47][48][49][50][51][52][53][54][55]. For instance, it has been found that for multi-qubit systems, the degree of entanglement robustness tends to increases or decreases with the increase of the number of qubits of the system [8,56]. In particular, the dynamics of quantum correlations in terms of entanglement and discord in a physical model of three non-interacting qubits subject to a classical environmental noise has recently been investigated [57][58][59].…”