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Sep 14, 2023 at 15:43 comment added Quantum Mechanic Yes - that's why you have my upvote! But it's true that mathematically it can look like something happens at a distance ($U\otimes I$ really produces the same effect as $I\otimes U^*$ when acting on a maximally entangled state), it's just that no information can be transmitted and you'll never be able to measure anything to have happened, so for the purpose of describing reality it is easiest to say that nothing happens
Sep 14, 2023 at 9:48 comment added Mateus Araújo That's true, but I'm afraid one can read your answer and conclude that there is some action at a distance, but there's also some elaborate conspiracy to prevent you from ever seeing it manifest. That's why I felt compelled to post another answer emphasizing that this is not the case.
Sep 13, 2023 at 19:25 comment added Quantum Mechanic Agreed. A fun thing to add is when we talk about operations other than measurement. As pointed out in this recent question quantumcomputing.stackexchange.com/q/34128/15820, maximally entangled states have the peculiar property that a local operation on one can instead be interpretted as a local operation on the other. That's what I tried to address in my answer: why, even with this local change, it is impossible to actually know that such a local unitary has been applied
Sep 13, 2023 at 8:56 history answered Mateus Araújo CC BY-SA 4.0