qics.quantum.purify

qics.quantum.purify(X)

Returns a purification of a quantum state \(X\). If \(X\) has spectral decomposition

\[X = \sum_{i=1}^n \lambda_i | v_i \rangle\langle v_i |,\]

then the purification is \(| \psi \rangle\langle \psi |\) where

\[| \psi \rangle = \sum_{i=1}^n \sqrt{\lambda_i} (| v_i \rangle \otimes | v_i \rangle).\]

Parameters:

Xndarray

Symmetric or Hermitian array of size (n, n) representing the matrix \(X\) we want to find the purification of.

Returns:

ndarray

Symmetric or Hermitian array of size (n*n, n*n) representing the purification of \(X\).