You wouldn't want the recreation to really be like your ex-girlfriend, you'd want it to be like the idealized perception of her in your memory.
That's the thing though, it doesn't have to be created by you.
The computer can do it based on actual information about her. So you would end up with almost the exact same person, interacting in the same way as if the person was real.
And if we accept data as a person, then this holodeck experience would be no less real than the flesh and blood person.