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You are an astronaut, traveling through space, but you ran out of fuel and need to get a hold of Houston immediately. How do you do it? You previously gave Houston one of two quantum particles that have been entangled. At the moment of distress you would change one of the particles, so the other would do the same and the distress call would be received.

Is such a system possible? Can we use quantum entanglement to send information instantaneously? If I remember correctly I though there also was a law stating that no information can travel faster than the speed of light. Or maybe I have that idea wrong.

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As Wolphram already stated, no information can be communicated via local measurements on entangled systems. We are so certain that this is true that this fact is considered as one of the so called No-go theorems, called the no-communication theorem.

The reason this is true is any measurement of one part of an entangled system is completely random. So what you measure and what Houston measures will always be completely random no matter what the other party does or doesn't do. It is only when you compare your results that you notice that your random results are correlated with Houston's random results (using normal communication which is limited to the speed of light).

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There is no way to send information using entangled particles. For instance , in your example, Houston is unable to know if you have already made a measurement. All it can do is make it own measurement whenever he wants, and then conclude what your measurement will be or was if you already measured it.

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