Noise effects in perfect transmission of quantum states

A recent scheme for perfect transmission of quantum states through quasi-one-dimensional chains requires application of global control at regular intervals of time. We study the effect of stochastic noise in this control and find that the scheme is robust for reasonable values of disorder. Both uncorrelated and correlated noise in the external control are studied, and it is remarkably found that the efficiency of the protocol is much higher in the presence of correlated noise.

Figure 1

(top) The quasi-one-dimensional chain introduced in [27]; solid lines indicate bonds with coupling equal to 1, and dashed lines are those with coupling equal to $-1$. (bottom) Its equivalent description in terms of two- and three-site perfect state transfer chains.

Figure 2

Average fidelity for various values of ${\epsilon }_{\theta }={\epsilon }_{\tau }=\epsilon$ in terms the chain length: (left) for a short chains of length up to $\approx$60 and (right) for long chains of length up to $\approx$1200, $N\approx 3K$. From top to bottom, $\epsilon =0.01,0.02,0.04,$ and $0.06$. The dashed line represent a fidelity of 0.95, and the dotted line represents the maximum fidelity, $F=2/3$, reached using a classical communication line.

Figure 3

Average fidelity for various values of $q$ in terms of the error probability $p$. From bottom to top, $q=0$ (no correlation), $0.9$, and 1 (full correlation). For all the curves $\epsilon =0.5$ and $K=100$.