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There are two types of information in physics: Classical information Quantum information Physics doesn't answer the question "What is (classical or quantum) information?". This is philosophic question, and physics never answers questions of this kind. Instead, physics answers another question "How (classical or quantum) information is measured?". The ...

It takes an infinite amount of information to specify the state of a qubit. That's for the reason you said: those two angles to specify the point on the Bloch sphere are continuous, and that means you need an infinite amount of precision. That being said, only one bit of accessible information is gained by measuring a qubit. If you had enough time and ...