“...distinguish whether it is purposefully transmitted information or random noise...” - that was solved for noisy analog commo last century; every character has a prefix, no prefix, then it’s not a character, it’s just noise. Very slow, but it worked.
Well, you also have an additional problem with quantum states, in that you have to measure them to receive the message, and measuring them changes the state of the entangled system. So you can’t just be a passive receiver like if you leave a radio turned on waiting for the message. Has the state changed because someone on the other side is sending a message? Or has it just changed because of the last time you took a measurement?
And you can’t just measure once to check for a “prefix”, since you are limited to a very few manipulations of quantum systems, so you can only send bits (or qbits) of information. A prefix can’t just be a “zero” or a “one” but would have to be a unique string of such data, and that means you would have to take multiple measurements (each changing the system) to check for a prefix. I don’t think that’s workable.