Physicists spooked by faster-than-light information transfer

I once thought I had invented a FTL communication mechanism. My idea was to make huge numbers of pairs of entangled particles (e.g. photons), and send each half of the pairs to one side of the communication line. Then, use this weird quantum trick to set the state of the pair on one side, and read it out on the other side. I know now that unfortunately, it's not possible. This is one of the hard-to-understand parts of quantum mechanics, but it's a classic one, so I guess the real experts should not expect FTL communication here.

The idea is that in quantum mechanics, it's not possible to know some things simultaneously. E.g., you can't both know position and momentum of a particle with infinite precision. Once you measure position, your measurement messes up the state of the particle, so that you can't measure the original momentum of the particle. In fact, the state (or wavefunction) becomes such that momentum isn't a well-defined property of the particle anymore. You can still do the measurement, but the outcome is random.

Now, it turns out to be possible to couple the state of particles, in a way that, even when you don't know a certain property of the particles (e.g. its spin), you still know it has to be related to the state of the other particle. You can know this because of laws like conservation of energy and momentum. Now, this sounds like it could be used to "cheat" on the first rule, as you might do the measurement of one property on one of the particles, and the measurement of another "incompatible" property on the other particle. Unfortunately, once you do the measurement on the first particle, the state of both particles turns out to be "messed up". This seems to happen immediately, no matter how far away the particles are.

So, this can make you think you can use it to cheat on the "no FTL communication" law. Unfortunately, the change of state can not be used for communication, because the outcome of the second measurement is random. It can not be influenced by the sender, and even if the sender chooses between measuring and not measuring (which would mean either a random or a non-random measurement at the receiver), the receiver has no way of distinguishing between random and non-random measurements, until the sender gives more information over a conventional (non-FTL) communication channel.

If you know a trick, please let me know. I can tell you the exact rules of the game for electron spins in orthogonal directions (which are "incompatible" properties). They are quite simple, but this post is already a bit too long.
 
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