Negativity and quantum discord in Davies environments

We investigate the time evolution of negativity and quantum discord for a pair of non-interacting qubits with one being weakly coupled to a decohering Davies-type Markovian environment. At initial time of preparation, the qubits are prepared in one of the maximally entangled pure Bell states. In the limiting case of pure decoherence (i.e. pure dephasing), both the quantum discord and negativity decay to zero in the long time limit. In the presence of a manifest dissipative dynamics, the entanglement negativity undergoes a sudden death at finite time, while the quantum discord relaxes continuously to zero with increasing time. We find that in dephasing environments, the decay of the negativity is more propitious with increasing time; in contrast, the evolving decay of the quantum discord proceeds more weakly for dissipative environments. Particularly, the slowest decay of the quantum discord emerges when the energy relaxation time matches the dephasing time.