qics.cones.ClassEntr

class qics.cones.ClassEntr(n)

A class representing a (homogenized) classical entropy cone

\[\mathcal{CE}_{n} = \text{cl}\{ (t, u, x) \in \mathbb{R} \times \mathbb{R}_{++} \times \mathbb{R}^n_{++} : t \geq -u H(u^{-1}x) \},\]

where

\[H(x) = -\sum_{i=1}^n x_i \log(x_i),\]

is the classical (Shannon) entropy function.

Parameters:

nint

Dimension of the vector \(x\), i.e., how many terms are in the classical entropy function.

See also

ClassRelEntr

Classical relative entropy cone

QuantEntr

(Homogenized) quantum entropy cone

Notes

The epigraph of the classical entropy can be obtained by enforcing the linear constraint \(u=1\).

Additionally, the exponential cone

\[\mathcal{E}=\{ (x,y,z)\in\mathbb{R}_+\times\mathbb{R}_+ \times\mathbb{R} : y \geq x \exp(z/x) \},\]

can be modelled by realizing that if \((x,y,z)\in\mathcal{E}\), then \((-z, y, x)\in\mathcal{CE}_1\).