Transitions in the Communication Capacity of Dissipative Qubit Channels

The information transmission is studied for quantum channels in which the noise includes dissipative effects, more specifically, nonunitality. Noise is usually a nuisance but can sometimes be helpful. For these channels, the communication capacity is shown to increase with the dissipative component of the noise and may exhibit transitions beyond which it increases faster. The optimal states are constructed analytically as well as the pertaining “phase” diagram.

Figure 1

Optimal states (solid line) for $a=0.53$, $b=0.5$, and, respectively, $c=0.3$, $c=0.34$, and $c=0.4$. The unit circle is the intersection of the Bloch sphere with an arbitrary plane containing the (vertical) $z$ axis. It is mapped by the nonunital channel onto the inner ellipse. The crosses correspond to the image of the optimal states and the triangle to the image of their average.

Figure 2

Types of optimal states as a function of $a$ and $c$ for $b=0.5$. The boundaries of this “phase” diagram are determined analytically [cf. below (4, 5)].

Figure 3

Holevo capacity (${\chi }_{\mathcal{E}}$), total probability of occurrence of the pair of northern states ($p$), and $z$ component of their Bloch vector ($\beta$) as a function of $c$ for $a=0.53$, $b=0.5$. The corresponding analytical expressions are given by (9, 10, 11, 12, 13, 14). The dotted lines are displayed to help visualize the crossover between the optimal states of type A and B.