  Quantum decoherence effects in neutrinos, described by the open quantum
systems formalism, serve as a gateway to explore potential new physics,
including quantum gravity. Previous research extensively investigated these
effects across various neutrino sources, imposing stringent constraints on the
spontaneous loss of coherence. In this study, we demonstrate that even within
the Supernovae environment, where neutrinos are released as incoherent states,
quantum decoherence could influence the flavor equipartition of $3\nu$ mixing.
Additionally, we examine the potential energy dependence of quantum decoherence
parameters ($\Gamma = \Gamma_0 (E/E_0)^n$) with different power laws ($n = 0,
2, 5/2$). Our findings indicate that future-generation detectors (DUNE,
Hyper-K, and JUNO) can significantly constrain quantum decoherence effects
under different scenarios. For a Supernova located 10 kpc away from Earth, DUNE
could potentially establish $3\sigma$ bounds of $\Gamma \leq 6.2 \times
10^{-14}$ eV in the normal mass hierarchy (NH) scenario, while Hyper-K could
impose a $2\sigma$ limit of $\Gamma \leq 3.6 \times 10^{-14}$ eV for the
inverted mass hierarchy (IH) scenario with $n=0$ - assuming no energy exchange
between the neutrino subsystem and non-standard environment ($[H,V_p] = 0$).
These limits become even more restrictive for a closer Supernova. When we relax
the assumption of energy exchange ($[H,V_p] \neq 0$), for a 10 kpc SN, DUNE can
establish a $3\sigma$ limit of $\Gamma_8 \leq 4.2 \times 10^{-28}$ eV for NH,
while Hyper-K could constrain $\Gamma_8 \leq 1.3 \times 10^{-27}$ eV for IH
($n=0$) with $2\sigma$, representing the most stringent bounds reported to
date. Furthermore, we examine the impact of neutrino loss during propagation
for future Supernova detection.
