  We show theoretically that the measurement of a $\mathcal{PT}$-symmetric
non-Hermitian superconductor by angle-resolved photoelectron fluctuation
spectroscopy (ARPFS) provides a decisive signature. In fact, the signal is
negative in a single-band case in contrast to the ARPFS signal of Hermitian
superconductors. We suggest that the negative fluctuations can be explained by
a remarkable pairing phenomenon: If the interaction between electrons in this
$\mathcal{PT}$-symmetric non-Hermitian superconductor is attractive then the
interaction between holes (i.e. missing electrons) is repulsive and vice versa.
This difference in the sign of the interactions gives rise to negative cross
correlations. Here, we propose how such electron-electron interaction can occur
due to spatiotemporal modulation of the material. We also discuss the
observability of this signature in multi-band systems.
