Test the non-signaling principle Has the non-signaling principle in quantum  mechanics been tested experimentally? 
 A: The rigorous answer is that experimentally you can prove that something exists, not that something doesn't exist. We proved that the electron exist, because we found it. But about the non-signaling, we can do one type experiment, two types, three, etc. And if none of the three experiments transmits FTL (faster-than-light), can we conclude that no type of experiment whatsoever, would transmit FTL?
Only theoretically we can prove the non-signaling, experimentally we can test one more type of experiment, and one more type, etc.
And, theoretically, it was proved. Abner Shimony proved that whatever unitary transformation would lice do on her particle, no change would result on Bob's reduced matrix. Since then, this proof was done for less restrictive transformations.
Now, let me tell you the bottom line. In order to obtain FTL transmission we need a non-unitary transformation. Not any non-unitary transformation, but one of the type realized in the experiment done by Herzog, Rarity, Weinfurter and Zeilinger, PRL 72, 629. But the nature gives us such transformations with so low probabilities that we can't exploit them. Bob cannot know when did occur with Alice's particle the non-unitary transformation. 
Bottom line, it was proved by A. Peres that FTL transmission implies re-writing the past. 
A: The non-signaling principle stems from the fact that in our Universe the past cannot be re-written. In fact, a Universe in which the past can be re-written cannot exist, it is self-contradictory. Faster-than-light communication appears in some frame of coordinates as sending information backward in time.
