qics.quantum.p_tr¶

qics.quantum.p_tr(mat, dims, sys)[source]¶

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

\[X \otimes Y \mapsto \text{tr}[X] Y,\]

if sys=0, or

\[X \otimes Y \mapsto \text{tr}[Y] X,\]

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

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 trace of.
dimstuple of int: The dimensions (n0, n1, ..., nk-1) of the \(k\) subsystems.
sysint or tuple of int: Which of the \(k\) subsystems to trace out. Can define multiple subsystems to trace out.

Returns:

ndarray: The resulting matrix after taking the partial trace. Has dimension (n0*n1*...*nk-1 / nx, n0*n1*...*nk-1 / nx) where nx is the product of the dimensions of the subsystems that have been traced out.