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)

Abstract

The paper investigates the dynamics of entanglement and explores some geometrical characteristics of the trajectories in state space, in four-qubit Greenberger-Horne-Zeilinger (GHZ) -and W-type states, coupled to common and independent classical random telegraph noise (RTN) sources. It is shown from numerical simulations that: (i) the dynamics of entanglement depends drastically not only on the input configuration of the qubits and the presence or absence of memory effects, but also on whether the qubits are coupled to the RTN in a CE or IEs; (ii) a considerable amount of entanglement can be indefinitely trapped when the qubits are embedded in a CE; (iii) the CE configuration preserves better the entanglement initially shared between the qubits than the IEs configuration, however, for W-type states, there is a period of time and/or certain values of the purity for which, the opposite can be found. Thanks to the results obtained in our earlier works on three-qubit models, we are able to conclude that entanglement becomes more robustly protected from decay when the number of qubits of the system increases. Finally, we find that the trajectories in state space of the system quantified by the quantum Jensen Shannon divergence (QJSD) between the time-evolved states of the qubits and some reference states may be curvilinear or chaotic.

Tripartite Quantum Correlations under Power‐Law and Random Telegraph Noises: Collective Effects of Markovian and Non‐Markovian Classical Fields

“…The claim can be validated by looking at the previously studied various systems and situations where, preservation intervals are insignificant or less frequent. [ 20,21,24,35,36,55,56 ] We discovered that when Γ increases, the correlations between the qubits decrease. As the value of Γ increases, the curves shift from green to red causing a greater decay.…”

“…It is important to note that the final density matrices obtained for MMLR and NMLR given in Equations ( 14) and ( 15), both are completely different from those obtained for Gaussian and non-Gaussian noises studied in refs. [21,23,[35][36][37]43].…”

“…As seen by comparing previous results given in refs. [21,24,35,36,45,54,[57][58][59] to the current ones. Quantum correlations, coherence, and purity are all lost periodically when non-Markovian effects are maximized.…”

“…For instance, in the case of local channels, proper tuning of the noise phase and related parameters has been accomplished for optimal information preservation. [19][20][21] Besides all this, the local channels provide more degrees of freedom to analyze the dynamics of quantum systems. This will allow us to critically analyze the dynamical maps of the non-classical correlations versus the noise phase, related parameters, and system-environment coupling.…”

“…[20] Because of the RT noise, a variety of decay has been observed in bipartite, tripartite, multipartite and other hybrid quantum systems, where the systems become either separable or remain entangled under certain conditions given in refs. [21,[32][33][34][35][36][37]. From these references, we noticed the PWL noise causes a monotonic decay while the RT noise induces both exponential and oscillatory decay.…”