Analysis and minimization of bending losses in discrete quantum networks

We study theoretically the transfer of quantum information along bends in two-dimensional discrete lattices. Our analysis shows that the fidelity of the transfer decreases considerably as a result of interactions in the neighborhood of the bend. It is also demonstrated that such losses can be controlled efficiently by the inclusion of a defect. The present results are of relevance to various physical implementations of quantum networks, where geometric imperfections with finite spatial extent may arise as a result of bending, residual stress, etc.

Figure 1

(a) A bent quantum chain of $N$ sites. (b) A closeup of the bend. Green (solid) arrows denote NN interactions of strength ${\Omega }_{i,j}$. Red (dashed) arrows denote interactions beyond NNs, with the strongest one (of strength $g$) corresponding to the first neighbors of the corner site $\alpha$.

Figure 2

Performance of the bent chain 1 for various $N$. (a)–(d) The normalized probability of transfer $Q_i$, for the bent chain without (bars) and with ($\times$) corner defect. Corner sites: (a), (b) $\alpha =6$; (c) $\alpha =11$; (d) $\alpha =13$. (e) Time of transfer through the bent chain without (open symbols) and with (filed symbols) corner defect. (f) Optimal detunings of the defect corner site relative to the other sites [17].

Figure 3

As in Fig. 2 for chain 2.

Figure 4

Performance of bent chains for different positions of the corner, and for fixed $\kappa =0.4$. Different points for each $N$ are obtained by increasing $\alpha$ from 2 to $\lceil N/2\rceil$ with step 1 [16]. (a), (c) Protocol 1 and (b), (d) protocol 2.

Figure 5

Difference between successive eigenenergies of the Hamiltonians for $N=25$ and $\alpha =12$. (a) Protocol 1, $\kappa =0.5$; (b) protocol 2, $\kappa =0.3$.