Classical capacity / Definition
Holevo information
Definition statement
For a quantum channel $\mathcal{N}$, the Holevo information $\chi(\mathcal{N})$ is the supremum of the Holevo quantity over all finite input ensembles:$$
\chi(\mathcal{N}) := \sup_{\{p_X(x),\rho_x\}}\left[H\!\left(\sum_x p_X(x)\,\mathcal{N}(\rho_x)\right) - \sum_x p_X(x)\,H\!(\mathcal{N}(\rho_x))\right]\!.
$$
Sources
- From Classical to Quantum Shannon Theory
Mark M. Wilde, 2011
Lean context
- Import
QIT.Coding.Classical.HSW- Lean declaration
QIT.Channel.holevoInformation
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