b_{u}- l _{u}$ when the current through the Josephson junctions does not exceed the critical current $I _{a}$ and $I _{b}$. Then, the superconducting current between $l _{u}$ and $r _{d}$ is equal to: $$I _{s} = I _{a}\sin  \varphi _{a} + I _{b}\sin  (\varphi _{a}+ \pi (n _{u} + n _{d})) \eqno{(6)}$$ The critical current $I _{c,DD}$ of the DDCI, i.e. the maximum value of the superconducting current (6), depends only on parity of the quantum number sum, and it does not explicitly depend on the magnetic flux, which makes the system to be an ideal detector of the quantum states. The critical current has only two values at $I _{a}= I _{b} = I _{cj}$ according to (6): $I _{c,DD} = 2 I _{c,j}$ when the sum $n _{u} + n _{d}$ of the quantum numbers of the upper loop $n _{u}$ and the bottom loop $n _{d}$ is even and $I _{c} = 0$ when it is odd. Therefore, for example at $\Phi = 0.5 \Phi _{0} + \delta \Phi $, the maximum value of the superconducting current (6) and the voltage measured on the DDCI at a bias current $I$ may change by jump when the 