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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.

ersbygre1
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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).

tparker
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