Noise-Enhanced Classical and Quantum Capacities in Communication Networks

The unavoidable presence of noise is thought to be one of the major problems to solve in order to pave the way for implementing quantum information technologies in realistic physical platforms. However, here we show a clear example in which noise, in terms of dephasing, may enhance the capability of transmitting not only classical but also quantum information, encoded in quantum systems, through communication networks. In particular, we find analytically and numerically the quantum and classical capacities for a large family of quantum channels and show that these information transmission rates can be strongly enhanced by introducing dephasing noise in the complex network dynamics.

Figure 1

Communication network: on one side, Alice sends a message encoded in the qubit 1 while the rest of the network is prepared in its ground state. On the other side, after the network noisy evolution, Bob tries to recover Alice’s message decoding the output in site $N$.

Figure 2

Classical and quantum capacities, $C_1[\mathcal{E}(\eta ,s)]$ and $Q_1[\mathcal{E}(\eta ,s)]$, vs $\eta$ and $s$. Inset: contour plot for $Q_1[\mathcal{E}(\eta ,s)]$ vs $s$ and $\eta$ in a color gradient scheme where light grey corresponds to 1 and black to vanishing values of $Q_1$. Note that $Q$ is always zero for $\eta \le 1/2$ and any $s$.

Figure 3

Classical capacity of the FMO-complex quantum channel, $C_1\{\mathcal{E}[p_{\mathrm{sink}}(t_{\mathrm{out}}),0]\}$, vs time $t_{\mathrm{out}}$. There is a clear remarkable enhancement of $C_1$ in the case of pure dephasing noise. By maximizing $C_1$ over $t_{\mathrm{out}}$, one has ${\overline{C}}_1(\mathcal{E})\sim 0.72$ in absence of dephasing, while ${\overline{C}}_1(\mathcal{E})\sim 0.99$ in the case of dephasing.

Figure 4

Quantum capacity $Q_1$ for a three-site network vs time $t_{\mathrm{out}}$. In the absence of noise, $Q$ is always zero, while $Q_1$ can get values almost up to one in the presence of dephasing. Here, the hopping and dephasing rates are $v_{12}=v_{23}=v_{13}=1$, and ${\gamma }_2=50$, ${\gamma }_1={\gamma }_3=0$. The corresponding channel entropy and fidelity are also shown in the noiseless (dashed) and dephasing (continuous line) case. In particular, ${\overline{Q}}_1(\mathcal{E})=0$ without noise, while ${\overline{Q}}_1(\mathcal{E})\sim 0.8$ with ${\gamma }_2=50$ and is monotonically increasing to 1 for higher dephasing rates.