Yes and no.
Probability is very important, but it is not the measurement, or at least not the initial measurements, which are the issue.
The measurements on the particles will actually be the spookily transmitted values that you would expect. If person A observes his particle and locks in a state, the particle of person B will instantly take on the mirror or opposite of what person A has measured. Until entanglement is broken, particle B will remain in that state for person B to discover almost at their leisure. So, you *can* measure two particles and get the same/mirror answer... but only once per particle.
Or in other words, if Person A observes a living Schrodinger's Cat in his box, Person B will get a dead one in his entangled box instantly, which will be there for him to see when he opens the box. It will not go back to being uncertain until the box is opened and then closed again. Person B does get the opportunity to see the state of his particle as changed by entanglement.
So what is the problem? Sounds like this is faster than light. And it is. However, Relativity does not state that nothing can happen faster than light, only that *information* cannot be transmitted faster than light. The problem is entanglement does not actually create a channel for passing information by itself.
For information to be passed one side must use a channel to send a message to the other. With entanglement you will have "sent" a state, but the other side has no way of knowing you actually sent a message, which in turn means that information is not passed.
Remember, collapsing the probabilities and killing/not killing a cat can be done by *either side*. That means that if you open your box and find a living cat, it could mean that your partner earlier opened his box and found his cat was dead (and is attempting to send you a message). Alternately, it might mean he hadn't gotten around to opening his box yet and you opened first, making you are responsible for killing his cat which he may soon discover (you monster).
This is *not* insurmountable normally. If you could, say, ensure that you always kill the cat in your box when you are sending a message, then I could use frequency analysis or some other algorithm on all of my living cat results because I know that only living cats can be message data. There would still be a ratio of noise to the signal due to the ever present possibility that I am killing his cat on the other side by looking before he does, but you should be able to wring data out of it. You would, of course, need multiple entangled boxes for this, but other than representing mass cat murder, this is not a major problem.
Unfortunately, this is where the Uncertainty Principle checkmates us. When you open a box, it is always completely random what you get. You can't force a result or know ahead of time what you will send, so pre-arranging to only accept one result is pointless. Even the smallest attempt to alter the box before opening it in a manner that would make the result even slightly more predictable counts as a measurement and trips the entanglement effect. Then when you go to look in the box afterward, you are simply looking at particle that is no longer entangled. In effect, altering the box in any useful way is the same thing as opening it.
So, to actually send a decipherable message, you need a classical, slower than light channel to decipher every bit of information you send via entangled particles. While it is technically true that your actual bits arrived faster than light, the information is 100% indecipherable until you get the decoder for each bit at light speed, and so there is no way to disseminate actual information faster than light in this way.
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