An inequality between the norm of the difference of two vector states of a W* -algebra and the infimum distance between vectors representing the states in a fixed representation is derived.
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Huzihiro Araki, A Remark on Bures Distance Function Remark on Bures Distance Function. Publ. Res. Inst. Math. Sci. 6 (1970), no. 3, pp. 477–482DOI 10.2977/PRIMS/1195193916