Algorithm 1 ObservableState.

Require:$Q_{ij}$, n. Step 1. For each$k\in [1,\dots ,({log}_{2}n+1)n]$ generate uniformly value $\rho \in [0,1]$ If${\rho <\left|\alpha \right|}^2$then$q_k=1$else$q_k=0$ and obtain the binary string: $[q_1{q}_2,\cdots q_{({log}_{2}n+1)n}]$. For each$i\in [1,\cdots n]$ translate the binary substring $[q_{i+1}{q}_{i+2}\cdots q_{i+({log}_{2}n+1)n}]$ to the decimal value and obtain the string of the decimal number $S_d=[d_1{d}_2\cdots d_n]$. Step 2. Replace each number $d_i$ in this way that the $S_d$ takes a permutation form. For $i=1$ to n do: Find the set of smallest, not marked, elements in the string $S_d=[d_1{d}_2\dots d_n]$. Replace the smallest element from the left side of the string - $d_k$, by the value i and set the value i at the position k as marked. Return string $S_d$ which has a permutation form.