The method you are referring to depends not on splitting a particle, but splitting an entangled state of two particles. It is possible to produce two particles in a state such that if one is polarized this way, the other is necessarily polarized that way. So if you were to separate the particles, and measured the polarization state of one, you would automatically know the polarization state of the other.
This has been used by science fiction authors to instantiate the old sf idea of the ansible, or instant communicator. The word ansible goes back to the science fiction of the 1960's and has been used continuously ever since.
Would it work? No. The idea is that if you flip the particle here from the orientation you brought it with, to the opposite one, then the other particle, over in the Alpha Centauri system, will also flip - in the opposiite direction, and thus you have sent a bit from here to Alpha, and if you can send bits then you can send messages.
But the particles come to you with every possible orientation. If you flip a random one, the other one is random too, and your message is lost in noise. And how do you know your own particle flipped. You can't know what state it's in - remember they come to you in all possible states - unless you look at it. And here we come to the killer fact:
If you look at either of the particles, if you interact with it in any way whatsoever, you destroy the entanglement
It's called collapse of the wave function. It was the wave function that carried the entanglement.
So you're hoist on the horns of a dilemma. Either you check the particle to see how it's oriented so you can flip it - in which case you have no more entanglement and the bit won't be sent, or you flip it blindly in which case the receiver at the other end can't tell which particle you flipped or which way is a flip.
But maybe you're clever. You say, I won't use random particles, I'll use particles all oriented in a certain direction, by agreement. So I won't have to look first, and my friend on Alpha will know what a flip is. But the process that produces entangled particles produces them with all possible orientations, and there are symmetry arguments that say this has to be. So to get the particles to line up in some fixed way you'ld have to act on them - ooops! there goes your entanglement again!
Bottom line. There ain't no such thing as a working ansible.