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.?
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It's not that there's a "rule" against superluminal information transfer. I'm not sure what that even means. It's just that if you actually work out what happens when you have entangled quantum objects you find that there just isn't any trick for sending a deterministic message. It's not an external rule, it's built into quantum mechanics. – DanielSank Nov 26 '14 at 20:19
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1You might want to look at http://physics.stackexchange.com/q/148761/ where this has been discussed. We can't send a message directly by this technique, but we can use the information sent between two parties to enable secure communications between the two of them. – tom Nov 26 '14 at 21:19
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5Possible duplicate of The choice of measurement basis on one half of an entangled state affects the other half. Can this be used to communicate faster than light? – knzhou Dec 14 '18 at 13:14
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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Nice answer. What always bothered me though is that quantum mechanics is not explicitly relativistic, there is no built-in speed limit, so this "agreement" with relativity is an accident. Moreover, having a "process" like collapse that appears to be instantaneous, and then finding out that the rest of the rules "conspire" to make it unusable for transfer of information or energy is uncomfortably similar to Lorentz's ether with length contractions and time dilations making it absolutely undetectable. It suggests that in a "correct" formulation of QM collapse, like ether, should be eliminated. – Conifold Nov 26 '14 at 22:47
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I wouldn't really say this is in agreement with relativity. More like it doesn't disagree with relativity. In particular, there is no hard speed limit here. All this says is that you can't transmit information instantaneously, but this argument doesn't show that you can't send it faster than the speed of light. – Jonathan Gleason Nov 26 '14 at 22:51
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Also, I don't think collapse is truly instantaneous. As a matter of fact, I don't think the notion that it be instantaneous even really makes sense. How would one show, experimentally, that this is instantaneous? You can measure again as fast as you can immediately after your first measurement, but there will always be a non-zero amount of time between these measurements. One would need to show that the correlation between the two measurements increased as we decreased the time between the measurements . . . but Heisenberg says that this cannot happen for the uncertainty will diverge! – Jonathan Gleason Nov 26 '14 at 22:56
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Thankyou all for your comments and answers, I think I understand now. I may have missinterpreted what I read in the article that stated this, it may have ment that no infomation can be transferred by entanglement in the form of communication. Not that no information can be transfured at all. Thanks for the clarification, – Kiah Nov 26 '14 at 23:49
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@Jonathan Gleason That's my point, collapse is postulated but when you try to measure anything about it something always gets in the way :). One can't even say what "triggers" it because the cut can always be moved. Decoherence goes in the right direction, but they have "universal wave function", which is even more like ether. – Conifold Nov 27 '14 at 00:08