  The recent supernova, SN 2023ixf, one of the closest observed type II SNe has
revealed the presence of a dense circumstellar material (CSM). Interaction of
the SN ejecta with this dense CSM might create high energy protons of PeV
energies through shock acceleration. These accelerated protons then colliding
with the CSM (inelastic $pp$ collision) can produce secondaries such as high
energy gamma-rays and neutrinos. However, no gamma-rays and neutrinos have been
detected by Fermi-LAT and IceCube from this event. Fermi-LAT has placed an
upper limit on the gamma-ray flux above $100$~MeV to be $2.6 \times
10^{-11}~\rm erg~cm^{-2}~s^{-1}$. On the other hand, IceCube's upper limit on
muon neutrino flux is $7.3\times 10^{-2} ~\rm GeV~cm^{-2}$. {\color{black}
Taking these limits into account and using the shock-CSM properties derived
from multi-wavelength observations, we obtain new upper limits on the gamma-ray
($10^{-11}~\rm erg~cm^{-2}~s^{-1}$) and neutrino ($10^{-3}~\rm GeV~cm^{-2}$)
fluxes from SN 2023ixf produced via the $pp$ interaction channel.} While we
found the gamma-ray flux to be consistent with Fermi-LAT's upper limit, the
neutrino flux is found to be about $2$ orders of magnitude smaller than the
IceCube's upper limit. We further analyse the detection prospects of such
secondary signals from future SN 2023 like events with upcoming detectors, CTA
and IceCube-Gen2 and found to have great discovery potential, if any similar
event occurs within $7$ Mpc.
