Some Black Ops 3 Zombies information has apparently been leaked by someone looking into the code of the PC version.
This Info includes
Theater Mode references confirm it’ll be available in zombies mode
References to a campaign and story mode for zombies
Game apparently checks your progress on Easter Eggs found in Black Ops 2 zombies, unclear as to why right now
Ranks and Prestige modes in Zombies (Activision has confirmed there is an XP progression system in Zombies)
In addition, theme music for the Zombies Menu and Shadows of Evil has leaked. You can listen HERE (link may probably be taken down soon).
Code suggesting that players can play as zombies (although a lot of code could be left over Black Ops 2 zombies)
The information above has not been confirmed by Activision or Treyarch.
Still yet to be confirmed. If it is however this zombies experience seems to be shaping up to be very good (fingers crossed).