What techniques are used to film the twins in Quantico?

After watching the show, I can say that most of the time we can't see both their faces in one shot. So it can be achieves by the Doppelganger method, as I explained in my other answer on the generic question about how double role scenes are shot:

The first thing you need to do is find someone who is about the same height as your main actor. Similar hair is also necessary, so whether the Doppelganger needs to dye his or her hair or wear a wig, that’s a judgment call.

Place the Doppelganger with his or her back to the camera and frame the shot to shoot over that person’s shoulder to focus on the main actor. Film it that way until you get what you want.

For the reverse of that shot, switch the hair and the outfit of the main actor and the Doppelganger and do the same thing on the other side. This way you can edit it so that you basically have the same person having a conversation with himself. - (Source: timidmonster.com)

And one more thing to note here is that one of them always had her hair covered by cloth; that can be a good method to achieve the hair-matching thing.

I do remember many scenes with both of them facing the camera, but this is also not practically impossible these days.

From my own answer on how it's done in Dhoom 3 (Bollywood film):

Aamir: With newer technology it becomes difficult for the actor, as the kind of shots you can design for a double role are limitless. Earlier due to constraints of technology, you could not touch each other in a double role. Physical contact could not be captured, as you would end up touching yourself on screen. The camera used to be pretty-much static and in wide. Here were are hugging each other, exchanging hats, one is giving an Apple to the other…Because with motion control cameras, you can duplicate the same moment a number of times. The angle and position are all locked in a computer, so a situation can be recreated identically, multiple times, for an actor to perform different shots for his respective character in a double role.

I did try to dig for the specific case of Quantico with no success.

Anyway a quite impressive answer on Quora says the following regarding how such scenes can be shot:

Several methods of doing it:

1. Split-screen: This is an old method and consist in physically cutting two negatives down the middle and putting them back together. It left a vertical line which needed to be masked somehow. Nowadays, with the digital editing software, you simply layer the two shots and put a mask over one of them. Since many post-production software packages let you animate masks, some simple interaction may be possible as long as the characters never obstruct one another. You can use also compositing software for more complicated shots.

2. Using a green-screen: You can shoot the scene with the actor playing the first role in the real set then shoot the same scene again with the same actor playing the second role against green screen then key him in the scene. If this involves camera movement then a motion-control rig would be necessary to exactly repeat the movement done in the first pass.

3. Face/head replacing: You have two actors who are very close physically (same body structure). They will act independently, but in post-production you take the face or head of one and put it on another one. That's how they did it in The Social Network with Arnie Hammer: http://popwatch.ew.com/2010/10/0... The same technique was applied in The Curious Case of Benjamin Button when they had a kids, a dwarf and a disabled actor all playing Brad Pitt's role, but they replaced their faces with Brad's.