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Suppose we have an entangled electron-positron pair that move really far apart. Alice, who measures the electron's spin, will either increase or decrease the price of a product, depending on whether she measures the spin as "up" or "down".

Bob at the positron detector knows that if he measures "up", the price of a certain product will decrease and if he measures "down", the price will increase. As soon as he measured the spin, he can start to buy or sell items of this product, depending on his result. However, the information that the price was changed by Alice travels at most with the speed of light to Bob's location. Therefore Bob has an advantage over other people at his location, because he already knows the information earlier.

How is this not transmitting information faster than the speed of light? I assume that the point is that Alice can not transfer any information she wants to Bob. Even if they used many entangled pairs, they could only react to a previously discussed plan.

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    $\begingroup$ What does this have to do with quantum mechanics? Alice and Bob's friend Sam gives them each a sealed package and tells them the packages contain identically colored tennis balls. They travel a great distance apart, Alice opens her package, she raises the price of the product if the ball is red and lowers it if the ball is blue. Bob opens his package, sees the color, and instantly knows what the price of the product. (Or at least knows the price of the product if Alice followed through on the plan, which he can't be sure of.) No QM needed; exact same scenario. $\endgroup$ – WillO Oct 5 '19 at 1:23
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Indeed there are games similar to this setup where separated player can use entanglement to perform better than is possible with classical communication. This is called "quantum pseudo-telepathy". As long as Alice and Bob agree on a strategy ahead of time, they can in certain setups "beat the classical system." But as you say, it doesn't count as "information transfer" because Alice can't choose the message to send to Bob.

As your thought experiment demonstrates, the exact meaning of the no-communication theorem is quite subtle, and quantum entanglement can indeed be used to "send information" in the loose colloquial sense of the phrase (although it can't be used to "send information" under a suitably careful definition of the phrase).

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  • $\begingroup$ "... because Alice can't choose the message to send to Bob." -- that makes the most sense to me, thank you! $\endgroup$ – Stephan Oct 5 '19 at 0:28
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It does not work that way, alice cannot know in advance the result of her measurement, so she cannot have control of what information she sends to bob via entanglement.

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