has anyone opened the 2-3 doors in the imperial prison, can only open with a key not lock pick. by imperial prison i mean the passage beneath the actual prison

I believe this is a quest from the dark brotherhood, the head honcho gives you a key to go and kill someone in a cell

Yes, and there is at least one other quest as well where you're given the key.

The doors that are locked you don't need to go near. That, and you just can't.

the doors is not for the dark brotherhood quest you have to jump on the pillars to get to the second level where there are at least three doors, one is in the one room where the emperor dies in the begining of the game you jump on the broken pillar and to the second level

not exactly in the room where the emperor died but the larger room from that one

While there may be a quest to send you back in there, do know that most of those doors don't actually do anything; if you examined them, they'd tell you that they lead to the very cell you are in! ("The Sanctum")

Where they actually lead is a little "closet" away from the rest of the map, that was simply tossed together to hold the assassins until they entered. The rooms look odd, as there are some gaps between the walls that lead into the void, and they have no ceiling.

If you want to see them for yourself, and are using the PC version, open the console, (press the [`] key) click on the door, and then type in, "unlock", and hit [enter]. This will remove the lock on the door, and let you use it.

thanks just curious

No problem.

Just a slight correction to what I said above: after checking it again, I've found that the doors typically go nowhere; if you get up close and examine them, they'll simply say "door;" unlocking them and attempting to open them will result in nothing happening.

What's happening here is that these doors are effectively "one-way;" They have a door-marker in front of them, that tells the game where the player/NPCs appear after passing through ANOTHER door, but the door you see does nothing.