Secret no Mukougawa

Seven years ago, Yuuto's older sister vanished through a mysterious door, leaving him with only a necklace. Now he has once again seen that same door, and watched two mysterious girls (Saya and Hina) go through it. Eager for clues about his sister's disappearance, he and his pet cat follow them through. However, he soon finds there's a reason his sister wouldn't let him come with her. In the deadly world on the other side of the door, his ignorance leads to tragedy. Now Saya insists that he travel through the door once again, to search for a way to retrieve the lives that he caused to be lost during his first journey.

(Source: MangaHelpers)