One-shot entropy tools / Theorem
Smooth min/max entropy duality
Theorem statement
Let $\rho_{ABC}$ be a pure subnormalized state and let $0 \le \varepsilon < \sqrt{\operatorname{Tr}\rho}$. Then $H_{\max}^{\varepsilon}(A|B)_{\rho} = -H_{\min}^{\varepsilon}(A|C)_{\rho}$.
Sources
- Quantum Information Processing with Finite Resources -- Mathematical Foundations
Marco Tomamichel, 2015
Lean context
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