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the professor provided an interesting question, which he felt demonstrated a violation of special relativity. Of course, this is most likely due to a lack of understanding on the professor's part, but neither I nor my friend know enough of entanglement to say what is wrong exactly.

Thought experiment:

Suppose you have two particles (A and B), each with two observables X and Y. A and B are in entangled states of X, but in pure states of Y. Moreover, these observables, X and Y, are non commuting.

Suppose an experimenter performs rapid and succesive measurements of observable Y on particle B. Then at some point the other observer makes a measurement of X on particle B.

Since the X states of both particles are entangled, a measurement of X on A will determine the state of B.

The professor argues that by measuring X on particle A this would create a change in the Y state of particle B (remember X and Y don't commute) (which is continually under measurement by the other experimenter) - and hence the observer of particle B will know that observer A has measured the state of his particle - a clear transmission of information instantenously.

It seems to me this argument relies on a faulty understanding of entanglement. I suspect that it's not possible to create a system in which only two of the variables are entangled - however none of my texts mention anything useful about entanglement. Griffith's only discusses entanglement of spins, but doesn't say one way or another whether or not the total angular momentum state has to be entangled as well, for instance.

Can someone guide me to some literature that will help illiuminate this argument?