Entanglement Dynamics and Symmetry Breaking in Symmetric four Qubits GHZ- and W-type States Coupled to Classical Random Telegraph Noise in Mixed Environments

Abstract

This paper investigates the time behavior of entanglement (quantified by negativity) and the symmetry breaking in a symmetric four-qubit system (initialized either in the GHZ-type or W-type states), interacting with a Markov and non-Markov random telegraph noise (RTN). Two different qubit-noise coupling configurations, namely C1 and C2 are investigated. In the first one (C1) it is assumed that, three of the qubits interact with the noise in a common environment (CE) and the remaining qubit in its own local environment while in the second one (C2) it is rather assumed that two of them interact in a CE and the rest also in their own CE. Using the entanglement between the different non-equivalent bipartitions of the qubits (obtained by dividing the system into two arbitrary blocks) as probe, it is demonstrated that the breaking of symmetry in the initialized state of the qubits occurs due to bipartitions of system in which none of the qubit(s) in the right block/partition share the same environment with the remaining qubit(s) in the left block/partition. On the other hand, it is shown that the CE induces an indirect interaction between the qubits which plays a constructive role in reducing the decay rate of entanglement. As a matter of fact, it is shown that the higher the number of qubit interacting in a CE, the more protected the entanglement of the overall system, demonstrating that the C1 scheme is more efficient for shield the system from the detrimental impacts induced by the RTN than the C2 one. Finally, it is shown that strong qubit-environment coupling strength also favors the exchanges of information between the qubits and the external environment.