Effects of quantum decoherence in a future supernova neutrino detection

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 $3\ensuremath{\nu}$ mixing. Additionally, we examine the potential energy dependence of quantum decoherence parameters ($\mathrm{\ensuremath{\Gamma}}={\mathrm{\ensuremath{\Gamma}}}_{0}(E/{E}_{0}{)}^{n}$) 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, if no quantum decoherence is observed, DUNE could potentially establish $3\ensuremath{\sigma}$ bounds of $\mathrm{\ensuremath{\Gamma}}\ensuremath{\le}6.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{eV}$ in the normal mass hierarchy (NH) scenario, while Hyper-K would impose a $2\ensuremath{\sigma}$ limit of $\mathrm{\ensuremath{\Gamma}}\ensuremath{\le}3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{eV}$ for the inverted mass hierarchy (IH) with $n=0$---assuming no energy exchange between the neutrino subsystem and nonstandard environment. These limits become even more restrictive for a closer supernova. When we relax the assumption of energy exchange, for a 10 kpc distance, DUNE could establish a $3\ensuremath{\sigma}$ limit of ${\mathrm{\ensuremath{\Gamma}}}_{8}\ensuremath{\le}4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}28}\text{ }\text{ }\mathrm{eV}$ for NH, while Hyper-K could constrain ${\mathrm{\ensuremath{\Gamma}}}_{8}\ensuremath{\le}1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}\text{ }\text{ }\mathrm{eV}$ for IH ($n=0$) with $2\ensuremath{\sigma}$, which would be orders of magnitude stronger than the bounds reported to date. Furthermore, we examine the impact of neutrino loss during propagation for future supernova detection.