qics.cones.QuantRelEntr

class qics.cones.QuantRelEntr(n, iscomplex=False)

A class representing a quantum relative entropy cone

\[\mathcal{QRE}_{n} = \text{cl}\{ (t, X, Y) \in \mathbb{R} \times \mathbb{H}^n_{++} \times \mathbb{H}^n_{++} : t \geq S(X \| Y) \},\]

where

\[S(X \| Y) = \text{tr}[X \log(X) - X \log(Y)],\]

is the quantum (Umegaki) relative entropy function.

Parameters:

nint

Dimension of the matrices \(X\) and \(Y\).

iscomplexbool

Whether the matrices \(X\) and \(Y\) are defined over \(\mathbb{H}^n\) (True), or restricted to \(\mathbb{S}^n\) (False). The default is False.

See also

ClassRelEntr

Classical relative entropy

QuantEntr

(Homogenized) quantum entropy cone

QuantCondEntr

Quantum conditional entropy cone

QuantKeyDist

Quantum key distribution cone