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)

TL;DR

This study examines how entanglement dynamics and state-space trajectories of four-qubit GHZ- and W-states are affected by common versus independent classical noise sources, revealing conditions for entanglement preservation and complex trajectory behaviors.

Contribution

It provides new insights into entanglement robustness and geometrical state-space characteristics in four-qubit systems under classical noise, extending previous three-qubit analyses.

Findings

Entanglement dynamics depend on qubit configuration and environment type.

Entanglement can be indefinitely trapped in common environment scenarios.

State-space trajectories can be curvilinear or chaotic, influenced by initial states and noise.

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 preserve better the entanglement initially shared between the qubits than the IEs, 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 results obtained in our earlier works on the three-qubit model, 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.