Origination and survival of qudit-qudit entanglement in open systems

The exact reduced dynamics for two independent qudits dephasingly coupled to a common zero-temperature, super-Ohmic, bosonic environment is studied. It is shown that the qudit-qudit subsystem initially prepared in a separable state evolves into an entangled state. Details of the entanglement origination depend on both the coupling strength and the spectral properties of the environment as well as on the dimension of the qudit; the environment-induced entanglement can survive in the long-time limit. The entanglement dynamics of initially maximally entangled qudit-qudit states is analyzed for two examples: the qubit-qubit and qutrit-qutrit systems. The theory is applied to negative partial transposition entangled states of a two-qutrit system, which are shown to be distillable (for the assumed initial state) for arbitrary environment parameters.