Why is it impossible to teleport quantum states?

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SUMMARY

Teleportation of quantum states is impossible due to the inherent nature of quantum measurement, which causes the collapse of the quantum state to a single observable value. When measuring a quantum state represented as a|0> + b|1>, where a and b are complex constants, the measurement yields only one bit of information (either 0 or 1), resulting in the loss of the original state. This loss of information prevents the reconstruction of the quantum state, as an infinite number of bits cannot be represented by a single bit. Therefore, the initial step of transforming a quantum state to classical information fails, making teleportation unfeasible.

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Wikipedia simply says that it is impossible to transform a quantum state to classical info and then back to the same state but doesn't really give a reason why. Can anybody explain in simple terms the reasoning behind this.
 
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When you measure a quantum state it collapses to one of sometimes many values for that observable. You cannot reconstruct the original state because information has been lost.
 
It's the first step that fails. An arbitrary quantum state of one qubit can be written a|0> + b|1>, where a and b are two complex constants. Because they're continuous they can have any value, and thus be said to represent an infinite number of bits of information. However, any measurement on the system, can only yield either 0 or 1, i.e. one single bit of information. Since an infinite number of bits can never be represented by one single bit, it's of course then clear that you can never copy an arbitrary quantum state to classical information if you only have a single copy of the quantum state to measure on.
 

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