I totally agree with Bill3, and I'd like to add a bit to it.

First of all, I think it is controlling behaviour to tell a person whom they should or should not be in touch with. It is entirely up to them whom they wish to talk to. Secondly, just because someone leaves her phone unlocked, it is nobody's business to go through it. That is a gross violation of privacy.

Having said that, it is the duty of your gf to ensure there won't be any objectionable item on her phone, should you ever check it. I think there is problematic behaviour on both sides. I'm not saying I don't understand your side. I once had a hunch about an ex and checked his chat with his ex on the sly. Sure enough, there were incriminating texts. Those and also the fact that I was sneaking around behind his back instead of asking him straight, showed the cracks in the foundation of our relationship. Two wrongs rarely make a right. My advice to you is to try to build a relationship without coercion or dishonesty. If that isn't possible with this person, it's time to call it quits.