Noise to lubricate qubit transfer in a spin network

We consider quantum state transfer in a fully connected spin network, in which the results indicate that it is impossible to achieve high fidelity by free dynamics. However, the addition of certain kinds of noise can be helpful for this purpose. In fact, we introduce a model of Gaussian white noise affecting the spin-spin couplings (edges), except those linked to the input and output node, and prove that it enhances the fidelity of state transfer. The observed noise benefit is scale free as it applies to a quantum network of any size. The amount of the fidelity enhancement, depending on the noise strength as well as on the number of edges to which it is applied, can be so high as to take the fidelity close to one.

Figure 1

Average fidelity $F_{\mathrm{io}}$ for state transfer between nodes 1 and 2 of the network with $n=4$ vs (dimensionless) time $t$ and (dimensionless) strength of the noise $\eta$ acting on the edge 3-4.

Figure 2

Density plot of the quantity $\Delta$ vs $n$ and (dimensionless) $t$ for $\eta =0.01$ and $m=n-2$. Lighter regions correspond to smaller values of $\Delta$ (with blank corresponding to 0).

Figure 3

Density plot of the quantity $\Delta$ vs $m(m-1)/2$ and (dimensionless) $t$ for $\eta =0.01$ and $n=10$. Lighter regions correspond to smaller values of $\Delta$ (with blank corresponding to 0).