## I. INTRODUCTION 

About twenty events of supernova neutrinos were detected from SN1987A [1, 2]. Some neutrino features such as neutrino temperatures and the energy carried out by neutrinos that had been obtained from the data of SN1987A were consistent with theoretical expectation [3–6]. However, the detected number of the neutrino events was still too small to find out more details about other flavors of the supernova neutrinos and the explosion mechanism. Although, we have not yet obtained neutrino events from the second core-collapse supernova which is the rare event of the century, detection of next supernova neutrinos is highly desirable to obtain important information on the neutrinos and the explosion mechanism. The expected information from the supernova neutrino observations is classified into two categories of implication for neutrino physics and for supernova physics. 

Large-volume underground detectors are now operating to detect various neutrino events. For example, Super-Kamiokande (SK), which is at the Kamioka mine in Japan, is a water Cherenkov detector, filled with 50,000 ton pure water (32,000 ton fiducial volume for the burst mode and 22,500 ton for the other modes) [7]. KamLAND is a liquid scintillator detector with 1,000 ton active volume [8]. Sudbury Neutrino Observatory (SNO) has oper- ated as a heavy water Cherenkov detector, filled with 1,000 ton fiducial volume [9]. Now, a new generation experiment, SNO+, is planned to be constructed [10]. We achieved re- markable development of the neutrino physics, especially about neutrino oscillation from the solar, atmospheric and reactor neutrino experiments with these detectors. In addition, the supernova neutrinos are thought to be fascinating targets of these detectors. If one supernova explodes at the Galactic center, thousands of neutrino events will be observed in Super-Kamiokande [11]. Furthermore, megaton-size neutrino detectors will detect × 10 5 supernova neutrino events in the future [12–16]. The neutrinos are released directly from the core, in which the extreme physical condition of very high density is realized. Therefore, the supernova neutrinos would become the probe of such an environment. 

Neutrino flavor change by the neutrino oscillations relates to neutrino oscillation param- eters, i.e., the mixing angles, mass hierarchy, and CP violation phase. Most of neutrino oscillation parameters have been determined by the various neutrino experiments [17–19]. However, the mixing angle θ$_{13}$ is not precisely constrained, and only the upper bound is known from reactor experiments (e.g., [20]). In addition, the neutrino mass hierarchy, i.e., 

