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In order to investigate the impact of collective neutrino oscillations (CNO)on the neutrino signal from a nearby supernova, we perform 3-flavor neutrinooscillation simulations employing the multiangle effect. The backgroundhydrodynamic model is based on the neutrino hydrodynamic simulation of a 8.8\Msun progenitor star. We find that CNO commences after some 100 ms postbounce. Before this, CNO is suppressed by matter-induced decoherence. In theinverted mass hierarchy, the spectrum of $\bar{\nu}_e$ becomes softer after theonset of CNO. To evaluate the detectability of this modification, we define ahardness ratio between the number of high energy neutrino events and low energyneutrino events adopting a fixed critical energy. We show that Hyper-Kamiokande(HK) can distinguish the effect of CNO for supernova distances out to $\sim 10$kpc. On the other hand, for the normal mass hierarchy, the spectrum of $\nu_e$becomes softer after the onset of CNO, and we show that DUNE can distinguishthis feature for supernova distances out to $\sim 10$ kpc. More work isnecessary to optimize the best value of critical energy for maximumsensitivity. We also show that if the spectrum of $\bar{\nu}_e$ in HK becomessofter due to CNO, the spectrum of $\nu_e$ in DUNE becomes harder, and viceversa. This synergistic observations in $\bar{\nu}_e$ and $\nu_e$, by HK andDUNE respectively, will be an intriguing opportunity to test the occurrence ofCNO.

Detectability of Collective Neutrino Oscillation Signatures in the Supernova Explosion of a 8.8 $M_\odot$ star