System-reservoir dynamics of quantum and classical correlations

We examine the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments. The most common noise channels (amplitude damping, phase damping, bit flip, bit-phase flip, and phase flip) are analyzed. By analytical and numerical analyses we find that, contrary to what is usually stated in the literature, decoherence may occur without entanglement between the system and the environment. We also show that, in some cases, the bipartite quantum correlation initially present in the system is completely evaporated and not transferred to the environments.

Figure 1

Correlation dynamics for the amplitude-damping channel considering partition $\mathit{AB}$ for the Werner initial state. (a) Classical correlation [Eq. (8)], (b) quantum correlation [Eq. (9)], (c) mutual information [Eq. (4)], and (d) concurrence [Eq. (27)].

Figure 2

Correlation dynamics for the amplitude-damping channel considering partition $E_A{E}_B$ for the Werner initial state. (a) Classical correlation [Eq. (8)], (b) quantum correlation [Eq. (9)], (c) mutual information [Eq. (4)], and (d) concurrence [Eq. (27)].

Figure 3

Correlation dynamics for the two-qubit system with the amplitude damping channel for the Werner state with (a) $\alpha =0.5$ and (b) $\alpha =0.6$. Quantum correlations given by Eq. (9) for partitions $\mathit{AB}$ (solid line) and $E_A{E}_B$ (dashed line) and entanglement given by Eq. (27) for partitions $\mathit{AB}$ (dotted line) and $E_A{E}_B$ (dot-dashed line).

Figure 4

Correlation dynamics for the amplitude-damping channel considering the partition ${\mathit{AE}}_A$ for the general state (22). Classical correlation (dot-dashed line) given by Eq. (8), quantum correlation (dotted line) given by Eq. (9), mutual information (solid line) given by Eq. (4), and concurrence (dashed line) given by Eq. (27).

Figure 5

Correlation dynamics for the amplitude-damping channel considering the partition ${\mathit{AE}}_B$ for the Werner initial state. (a) Classical correlation [Eq. (8)], (b) quantum correlation [Eq. (9)], (c) mutual information [Eq. (4)], and (d) entanglement [Eq. (27)].

Figure 6

Correlation dynamics for the dephasing channel considering the partition ${\mathit{AE}}_A$ for the general state (22). Classical correlation (dashed line) given by Eq. (8), quantum correlation (solid line) given by Eq. (9), and concurrence (dotted line) given by Eq. (27).

Figure 7

Correlation dynamics for the dephasing channel considering partition $E_A{E}_B$ for the general state (22). (a) Classical correlation [Eq. (8)], (b) quantum correlation [Eq. (9)], and (c) mutual information [Eq. (4)].

Figure 8

Correlation dynamics for the dephasing channel considering partition ${\mathit{AE}}_B$ for the general state (22). (a) Classical correlation [Eq. (8)], (b) quantum correlation [Eq. (9)], and (c) mutual information [Eq. (4)].

Figure 9

Correlation dynamics for the bit-flip channel considering the partition ${\mathit{AE}}_A$ for the general state (22). Classical correlation (dashed line) given by Eq. (8), quantum correlation (solid line) given by Eq. (9), and the concurrence (dotted line) given by Eq. (27).

Figure 10

Correlation dynamics for the bit-flip channel considering partition ${\mathit{AE}}_B$ for the general state (22). (a) Classical correlation [Eq. (8)], (b) quantum correlation [Eq. (9)], and (c) mutual information [Eq. (4)].

Figure 11

Correlation dynamics for the bit-flip channel considering partition $E_A{E}_B$ for the general state (22). (a) Classical correlation [Eq. (8)], (b) quantum correlation [Eq. (9)], and (c) mutual information [Eq. (4)].