toqito.channel_ops.partial_channel
==================================

.. py:module:: toqito.channel_ops.partial_channel

.. autoapi-nested-parse::

   Applies a channel to a subsystem of an operator.





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

.. py:function:: partial_channel(rho, phi_map, sys = 2, dim = None)

   Apply channel to a subsystem of an operator [@Watrous_2018_TQI].

   Applies the operator

   \[
       \left(\mathbb{I} \otimes \Phi \right) \left(\rho \right).
   \]

   In other words, it is the result of applying the channel \(\Phi\) to the second subsystem
   of \(\rho\), which is assumed to act on two subsystems of equal dimension.

   The input `phi_map` should be provided as a Choi matrix.

   This function is adapted from the QETLAB package.

   .. rubric:: Examples

   The following applies the completely depolarizing channel to the second
   subsystem of a random density matrix.

   ```python exec="1" source="above"
   import numpy as np
   from toqito.channel_ops import partial_channel
   from toqito.channels import depolarizing
   rho = np.array([
      [0.3101, -0.0220 - 0.0219j, -0.0671 - 0.0030j, -0.0170 - 0.0694j],
      [-0.0220 + 0.0219j, 0.1008, -0.0775 + 0.0492j, -0.0613 + 0.0529j],
      [-0.0671 + 0.0030j, -0.0775 - 0.0492j, 0.1361, 0.0602 + 0.0062j],
      [-0.0170 + 0.0694j, -0.0613 - 0.0529j, 0.0602 - 0.0062j, 0.4530]
   ])

   res = partial_channel(rho, depolarizing(2))

   np.set_printoptions(linewidth=150, suppress=False)
   print(res)
   ```



   The following applies the completely depolarizing channel to the first
   subsystem.

   ```python exec="1" source="above"
   import numpy as np
   from toqito.channel_ops import partial_channel
   from toqito.channels import depolarizing

   rho = np.array([
      [0.3101, -0.0220 - 0.0219j, -0.0671 - 0.0030j, -0.0170 - 0.0694j],
      [-0.0220 + 0.0219j, 0.1008, -0.0775 + 0.0492j, -0.0613 + 0.0529j],
      [-0.0671 + 0.0030j, -0.0775 - 0.0492j, 0.1361, 0.0602 + 0.0062j],
      [-0.0170 + 0.0694j, -0.0613 - 0.0529j, 0.0602 - 0.0062j, 0.4530]
   ])

   res = partial_channel(rho, depolarizing(2))
   np.set_printoptions(linewidth=150, suppress=False)
   print(res)
   ```

   :raises ValueError: If Phi map is not provided as a Choi matrix or Kraus operators.

   :param rho: A matrix.
   :param phi_map: The map to partially apply.
   :param sys: Scalar or vector specifying the size of the subsystems.
   :param dim: Dimension of the subsystems. If `None`, all dimensions are assumed to be equal.

   :returns: The partial map `phi_map` applied to matrix `rho`.