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What classical information is carried by $\alpha|0\rangle+\beta|1\rangle$ and $\alpha|00\rangle+\beta|11\rangle$? How to quantify it? To be specific, A GHZ state, $\frac{1}{\sqrt 2}[|000\rangle+|111\rangle]$ can deterministically teleport both the states. Both the states appears to be same from the teleportation point of view. Does they carry same information?

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The result of measuring a quantum superposition is always a bit of information. One cannot see more than one answer if one looks. So when you speak of information carrying capacity, a qubit is a two-state quantum-mechanical system and so "carries " all possibilties, but we may find only either possible answer when we measure a qubit thus one bit of classical information is found because classical information is all that nature allows us to know.

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