All three versions of this quest need the same thing:
All quest triads start with the non-repeatable quest, which unlocks both of the repeatable quests. Almost, but not all, triad repeatable quests can be performed and turned in at the same time (this one can).
This page refers to content introduced in the expansion, Chapter VII: Legacy of the Soulless.
Examine the Magical Sword dropped by the Elite Demon Swordsman to start the quest An Ownerless Sword.