  The merging of a binary system involving two neutron stars (NSs), or a black
hole (BH) and a NS, often results in the emission of an electromagnetic (EM)
transient. One component of this EM transient is the epic explosion known as a
kilonova (KN). The characteristics of the KN emission can be used to probe the
equation of state (EoS) of NS matter responsible for its formation. We predict
KN light curves from computationally simulated BH-NS mergers, by using the 3D
radiative transfer code \texttt{POSSIS}. We investigate two EoSs spanning most
of the allowed range of the mass-radius diagram. We also consider a soft EoS
compatible with the observational data within the so-called 2-families scenario
in which hadronic stars coexist with strange stars. Computed results show that
the 2-families scenario, characterized by a soft EoS, should not produce a KN
unless the mass of the binary components are small ($M_{\rm BH} \leq
6M_{\odot}$, $M_{\rm NS} \leq 1.4M_{\odot}$) and the BH is rapidly spinning
($\chi_{\rm BH} \geq 0.3$). In contrast, a strong KN signal potentially
observable from future surveys (e.g. VRO/LSST) is produced in the 1-family
scenario for a wider region of the parameter space, and even for non-rotating
BHs ($\chi_{\rm BH} = 0$) when $M_{\rm BH} = 4M_{\odot}$ and $M_{\rm NS} =
1.2M_{\odot}$. We also provide a fit that allows for the calculation of the
unbound mass from the observed KN magnitude, without running timely and costly
radiative transfer simulations. Findings presented in this paper will be used
to interpret light curves anticipated during the fourth observing run (O4), of
the advanced LIGO, advanced Virgo and KAGRA interferometers and thus to
constrain the EoS of NS matter.
