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How do the state spaces of a single qubit and a particle moving on a line (the wavefunction case) differ?
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A qubit lives in L^2(R) while a particle on a line lives in C^2; the wavefunction is the simpler of the two
A qubit lives in the 2-dimensional space C^2 (two complex amplitudes); a particle on a line lives in the infinite-dimensional space L^2(R) of square-integrable functions
Both live in C^2, since every quantum system has exactly two basis states
A qubit lives in C^2 and a particle on a line lives in C^3, one complex amplitude per spatial dimension
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