with a VSS scheme. []{data-label="fig_gen"}](fig_general_scenario){width="1\columnwidth"}

Let us illustrate this point with a simple example. In particular, let us consider, for instance, the error correction step in QKD. Here, say Bob wants to correct a certain bit string, $k_{\rm B, key}$, to match that of Alice, which we shall denote by $k_{\rm A, key}$. In general, this process requires that both Alice and Bob first apply certain error correction matrices, $M_{\rm EC}$, to $k_{\rm B, key}$ and $k_{\rm A, key}$ to obtain the syndrome information $s_{\rm A}=M_{\rm EC}k_{\rm A, key}$ and $s_{\rm B}=M_{\rm EC}k_{\rm B, key}$, respectively. Afterward, if $s_{\rm A}\neq{}s_{\rm B}$ Bob modifies $k_{\rm B, key}$ accordingly. This process is then repeated a few times until it is guaranteed that $k_{\rm B, key}=k_{\rm A, key}$ with high probability. Let us now consider again the same procedure but now acting on shares, $k_{\rm A{\it j}, key}$ and $k_{\rm B{\it j}, key}$, of $k_{\rm A, key}$ and $k_{\rm B, key}$ respectively. That is, say $k_{\rm A, key}=\oplus_j^q k_{\rm A{\it j}, key}$ and $k_{\rm B, key}=\oplus_j^q k_{\rm B{\it j}, key}$, with $q$ being the total number of shares. For this, Alice and Bob first apply $M_{\rm EC}$ to $k_{\rm A{\it j}, key}$ and 