How many orthonormal bases are needed to distinguish all pure quantum states?
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- Carmeli, C., Heinosaari, T., Schultz, J. et al. Eur. Phys. J. D (2015) 69: 179. doi:10.1140/epjd/e2015-60230-5
We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d = 2 the answer is three. For the dimensions d = 3 and d ≥ 5 the answer is four. For the dimension d = 4 the answer is either three or four. Curiously, the exact number in d = 4 seems to be an open problem.