toqito.channels.reduction
=========================

.. py:module:: toqito.channels.reduction

.. autoapi-nested-parse::

   Generates the reduction channel.





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

.. py:function:: reduction(dim, k = 1)

   Produce the reduction map or reduction channel [@WikiReductionCrit].

   If `k = 1`, this returns the Choi matrix of the reduction map which is a positive map
   on `dim`-by-`dim` matrices. For a different value of `k`, this yields the
   Choi matrix of the map defined by:

   \[
       R(X) = k * \text{Tr}(X) * \mathbb{I} - X,
   \]

   where \(\mathbb{I}\) is the identity matrix. This map is \(k\)-positive.

   .. rubric:: Examples

   Using `|toqito⟩`, we can generate the \(3\)-dimensional (or standard) reduction map
   as follows.


   ```python exec="1" source="above"
   from toqito.channels import reduction

   print(reduction(3))
   ```

   :param dim: A positive integer (the dimension of the reduction map).
   :param k: If this positive integer is provided, the script will instead return the Choi matrix of the following
   :param linear map: Phi(X) := K * Tr(X)I - X.

   :returns: The reduction map.