qics.cones.QuantCondEntr¶

class qics.cones.QuantCondEntr(dims, sys, iscomplex=False)[source]¶

A class representing a quantum conditional entropy cone defined on \(k\) subsystems, where the \(i\)-th subsystem has dimension \(n_i\), and the \(i\)-th subsystem is being traced out, i.e.,

\[\mathcal{QCE}_{\{n_i\}, j} = \text{cl}\{ (t, X) \in \mathbb{R} \times \mathbb{H}^{\Pi_in_i}_{++} : t \geq -S(X) + S(\text{tr}_i(X)) \},\]

where

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

is the quantum (von Neumann) entropy, and \(\text{tr}_i\) is the partial trace on the \(i\)-th subsystem.

Parameters:

dimstuple of int or list of int: List of dimensions \(\{ n_i \}_{i=0}^{k-1}\) of the \(k\) subsystems.
sysint or tuple of int or list of int: Which systems are being traced out by the partial trace. Can define multiple subsystems to trace out.
iscomplexbool: Whether the matrix \(X\) is defined over \(\mathbb{H}^n\) (True), or restricted to \(\mathbb{S}^n\) (False). The default is False.