qics.quantum.partial_transpose

qics.quantum.partial_transpose(mat, dims, sys)

Performs the partial transpose on a multipartite matrix, e.g., for a bipartite state with dims=(n0, n1), the unique linear map satisfying

\[X \otimes Y \mapsto X^\top \otimes Y,\]

if sys=0, or

\[X \otimes Y \mapsto X \otimes Y^\top,\]

if sys=1, for all \(X,Y\in\mathbb{C}^{n\times n}\).

Parameters:

matndarray

Array of size (n0*n1*...*nk-1, n0*n1*...*nk-1) represnting a matrix defined on \(k\) subsystems which we want to take the partial transpose of.

dimstuple of int

The dimensions (n0, n1, ..., nk-1) of the \(k\) subsystems.

sysint

Which of the \(k\) subsystems to transpose.

Returns:

ndarray

The resulting (n0*n1*...*nk-1, n0*n1*...*nk-1) matrix after performing the partial transpose.