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

.. py:module:: channel_ops.partial_channel

.. autoapi-nested-parse::

   Applies a channel to a subsystem of an operator.



Functions
---------

.. autoapisummary::

   channel_ops.partial_channel.partial_channel


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

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

   Apply channel to a subsystem of an operator :cite:`Watrous_2018_TQI`.

   Applies the operator

   .. math::
       \left(\mathbb{I} \otimes \Phi \right) \left(\rho \right).

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

   The input :code:`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.

   .. jupyter-execute::

    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.

   .. jupyter-execute::

    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)


   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :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 :code:`None`, all dimensions
               are assumed to be equal.
   :return: The partial map :code:`phi_map` applied to matrix :code:`rho`.