when I was first introduced to entanglement I was told that "it is a phenomena that allows information to be transmitted faster than light", however, as I kept reading up on it, this seemed to be an oversimplified model to the extent of inaccuracy. I now find that there is a rule that says information cannot be transmitted this way... why? I understand that transmitting information via entanglement breaks relativity (in the sense that it means information can be transmitted then light). But surely things like the information loss paradox etc. have counter intuitive names if no information can actual be gained from these mechanisms. So, is there an intuitive way of explaining why no information can be transmitted this way (or if it can), other than it breaks down other theories.?
1 Answers
What makes you think that information can be transferred in this way in the first place? I cannot tell you why your method won't work if I don't know what method you have in mind. In any case, I can take a guess as to what you're referring to.
Suppose we have a pair of electrons in the state (up to normalization) $\left| +\right> \left| -\right> +\left| -\right> \left| +\right>$, where $\left| \pm \right>$ is the state of a single electron with spin up/down along the $z$-axis respectively, and the left-hand state will be the state of Alice's electron and the right-hand state will be the state of Bob's electron.
If Bob measures the spin of his electron, he has a $50$-$50$ chance of getting spin up or spin down. Without loss of generality, suppose that he measures spin up. This implies that, after Bob's measurement, the state of the entire system will be $\left| -\right> \left| +\right>$, and in particular, if Alice now makes a measurement, she will measure spin down with $100\%$ probability.
We, being omniscient in the sense that we know what the entire state before hand know this, but Alice did not know what the state was before measurement, and so there is no way for her to know what the state is after Bob's measurement! That is to say, we know she will measure spin down, but it is impossible for her to know this. Thus, you cannot use this method (or any similar variant) to transfer information.
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