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.

Figure 1

(Color online) Negativity vs dimensionless time of two identical qubits embedded in a super-Ohmic environment. The qubits are prepared in the separable initial state (30). Upper panel: influence of the spectral exponent $\mu$; the coupling strength $g_0=0.1$. Lower panel: influence of the coupling strength $g_0$; the spectral exponent $\mu =0.1$, ${\omega }_c={10}^2$, and ${\epsilon }_1={\epsilon }_2=1$.

Figure 2

(Color online) Negativity vs dimensionless time of two identical qutrits embedded in a super-Ohmic environment. The qutrits are prepared initially in the separable state (31). Upper panel: influence of the spectral exponent $\mu$; the coupling strength $g_0=0.1$. Lower panel: influence of the coupling strength $g_0$; the spectral exponent $\mu =0.1$, ${\omega }_c={10}^2$, and ${\epsilon }_1={\epsilon }_2=1$.

Figure 3

(Color online) Negativity vs dimensionless time of two qubits (upper panel) and two qutrits (lower panel) embedded in a super-Ohmic environment. The qudits are in the maximally entangled initial states given by Eq. (32) for qubits and Eq. (38) for qutrits. Influence of the spectral exponent is shown for several values of $\mu$; fixed ${\omega }_c={10}^2$, $g_0=0.01$, and ${\epsilon }_1={\epsilon }_2=1$.