Classical capacity / Theorem

Hayashi-Nagaoka operator inequality (c = 1)

Theorem statement

Let $A$ and $B$ be positive semidefinite operators with $A \le 1$. The Hayashi-Nagaoka operator inequality (parameter 1) gives $1 - (A+B)^{-1/2}\, A\, (A+B)^{-1/2} \;\le\; 2\,(1 - A) + 4\,B$.

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