How many orthonormal bases are needed to distinguish all pure quantum states?
: Claudio Carmeli, Teiko Heinosaari, Jussi Schultz, Alessandro Toigo
Publisher: SPRINGER
: 2015
: European Physical Journal D
: EUROPEAN PHYSICAL JOURNAL D
: EUR PHYS J D
: 179
: 69
: 7
: 11
: 1434-6060
DOI: https://doi.org/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.