Thanks. While you were writing your comment I found this article [0] that does a decent job of explaining why my hypothetical system isn't possible. It first lays out the exact system I had in mind and then unfortunately debunks it :(
I don't fully understand the subtleties, but the root problem seems to be that by measuring the state, you're perturbing the system and putting it into a new state, such that your measurement becomes irrelevant, as if you're always one step behind the message and can never catch up.
> The only way that this problem could be circumvented is if there existed some way of making a quantum measurement that actually forced a particular outcome. (Note: this is not something permitted within the presently-known laws of physics.)
I don't fully understand the subtleties, but the root problem seems to be that by measuring the state, you're perturbing the system and putting it into a new state, such that your measurement becomes irrelevant, as if you're always one step behind the message and can never catch up.
> The only way that this problem could be circumvented is if there existed some way of making a quantum measurement that actually forced a particular outcome. (Note: this is not something permitted within the presently-known laws of physics.)
[0] https://bigthink.com/starts-with-a-bang/quantum-entanglement...