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Some applications of the Hermite–Hadamard inequality for log‐convex functions in quantum divergences

One of the beautiful and very simple inequalities for a convex function is the Hermite–Hadamard inequality. The concept of log ‐convexity is a strong variant of convexity. In this paper, by the Hermite–Hadamard inequality, we introduce two‐parametric Tsallis quantum relative entropy, two‐parametric Tsallis–Lin quantum relative entropy, and two‐parametric quantum Jensen–Shannon divergence in quantum information theory. Then some properties of quantum Tsallis–Jensen–Shannon divergence for two density matrices are investigated by this inequality.