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On the Riemannian metric of α-entropies of density matrices

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The Riemannian metric induced by quantum α-entropies is proven to be monotone under stochastic mappings on the set of density matrices. The length of tangent vectors is essentially the Wigner-Yanase-Dyson skew information in this setting.

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Supported by the Hungarian National Foundation for Scientific Research, grant No. T-016924.

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Petz, D., Hasegawa, H. On the Riemannian metric of α-entropies of density matrices. Lett Math Phys 38, 221–225 (1996).

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