Abstract
Let [Formula: see text] be the space of n × n complex matrices endowed with the Hilbert–Schmidt scalar product, let Sn be the unit sphere of Mn and let Dn⊂ Mn be the space of strictly positive density matrices. We show that the scalar product over Dn introduced by Gibilisco and Isola3 (that is the scalar product induced by the map [Formula: see text]) coincides with the Wigner–Yanase monotone metric.
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