toqito.channel_ops.natural_representation
=========================================

.. py:module:: toqito.channel_ops.natural_representation

.. autoapi-nested-parse::

   Kraus operators to natural representation.





Module Contents
---------------

.. py:function:: natural_representation(kraus_ops)

   Convert a set of Kraus operators to the natural representation of a quantum channel.

   The natural representation of a quantum channel is given by:
   \(\Phi = \sum_i K_i \otimes K_i^*\)
   where \(K_i^*\) is the complex conjugate of \(K_i\).

   .. rubric:: Examples

   ```python exec="1" source="above"
   import numpy as np
   from toqito.channel_ops import natural_representation
   k0 = np.sqrt(1/2) * np.array([[1, 0], [0, 1]])
   k1 = np.sqrt(1/2) * np.array([[0, 1], [1, 0]])
   print(natural_representation([k0, k1]))
   ```