Topologically, classical bits (cbits) are essentially special cases of qubits restricted to the poles of the Bloch sphere. However, this restriction doesn't seem to be classical per se, but is simply inherited from the historical fact that transistors are either on or off. One could very well conceive of a classical bit which lives in a "classical" Bloch sphere of sorts, i.e., imagine some tiny, fully classical sphere with a needle that can point in all directions. Obviously, one of these dimensions won't be imaginary, but topologically speaking, it would be equivalent to the quantum Bloch sphere. E.g., if the needle were pointing along the equator, then we'd have a perfect example of classical superposition, which one could argue is "coherent" since it has a well defined phase and isn't the result of a statistical mixture.

I'll try to expand on the above with an example. Let's say our classical measurement basis is $NS$ (North $1$, South $0$) vs. $EW$ (East $1$, West $0$). To answer the question "*is the wind blowing in the $NW$ direction?*", we would need at least two measurements: One along the NS basis vector and the other along the $EW$ vector. If the results is $10$, then the answer is affirmative. However, would may as well apply a "classical Hadamard gate" which rotates the classical basis so as to answer the same question with a single measurement---as opposed to two---hence exhibiting the same "speedup" as what is typically purported to be unique to quantum superposition.

Ultimately, I'm looking for the "secret sauce" that qubits have that cbits don't. Clearly, there has to be more to it than what could be possible with my example of classical, analog Bloch spheres.

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***[Cross-posted on qc.SE](https://quantumcomputing.stackexchange.com/q/26014/55)***