Entanglement preservation of three qubits in a common reservoir via addition of qubits

Abstract

Under Markovian and non-Markovian regimes, we apply the method of adding qubits to preserve the entanglement of three qubits in an N-qubit system immersed in a common zero temperature Lorentzian reservoir composed of harmonic oscillators. From the reduced density matrix of the three qubits of interest, we determine whether the three qubits are entangled or not by using the separability criterion of Flores and Galapon [Ann. Phys. 392, 297 (2016)]. Moreover, we investigate the entanglement of three qubits as a function of time by the lower bound of concurrence (LBC). The first measure can only detect entanglement among three qubits at a certain time interval. Using the proposed scheme, the amount of entanglement, measured through concurrence, lost to the environment is lessened as the number of additional qubits is increased, hence, proving that such method is effective in protecting the entanglement.