A2 Refereed review article in a scientific journal
How many orthonormal bases are needed to distinguish all pure quantum states?
Authors: Claudio Carmeli, Teiko Heinosaari, Jussi Schultz, Alessandro Toigo
Publisher: SPRINGER
Publication year: 2015
Journal: European Physical Journal D
Journal name in source: EUROPEAN PHYSICAL JOURNAL D
Journal acronym: EUR PHYS J D
Article number: 179
Volume: 69
Issue: 7
Number of pages: 11
ISSN: 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.