Minimal Kitaev chains provide a unique platform to engineer Majorana states in quantum dots interacting via normal tunneling and crossed Andreev reflection specified by their amplitudes $|{\eta }_{n,a}|$. Here we analyze fluctuations of electric currents in a double quantum dot Kitaev chain using the differential effective charge $q$, that is the ratio of the differential shot noise and conductance. At low bias voltages $V$ we find that $q=e/2$ in a very narrow vicinity of the point $|{\eta }_n|=|{\eta }_a|$ whereas $q=3e/2$ almost in the whole sweet spot region and marks the range where the poor man's Majorana states largely govern the fluctuations. At high $V$ we show that the sweet spot region is still characterized by $q=3e/2$ uniquely identifying the poor man's Majorana states using the high voltage tails. For $|{\eta }_n|=0$ or $|{\eta }_a|=0$ we obtain $q=e$ at any $V$. Remarkably, before the asymptotic value $q=e$ is reached for very high $V$, the maximal value $q=2e$ is formed at $\left|eV\right|=2\sqrt{|{\eta }_n{|}^2+{\left|{\eta }_a\right|}^2}$. The unique nature and potentially rich fluctuation behavior revealed in this work provide a stimulating ground for the next generation experiments on nonequilibrium shot noise in minimal Kitaev chains.

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• Majorana bound states
• Quantum transport
• Shot noise
• Double quantum dots
• Superconductors
• Nonequilibrium Green's function
• Path-integral methods