:py:mod:`channel_props.is_unital`
=================================

.. py:module:: channel_props.is_unital

.. autoapi-nested-parse::

   Determine whether channel is unital.



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


Functions
~~~~~~~~~

.. autoapisummary::

   channel_props.is_unital.is_unital



.. py:function:: is_unital(phi, rtol = 1e-05, atol = 1e-08, dim = None)

   Determine whether the given channel is unital.

   A map :math:`\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)` is *unital* if it holds that:

   .. math::
       \Phi(\mathbb{I}_{\mathcal{X}}) = \mathbb{I}_{\mathcal{Y}}.

   If the input channel maps :math:`M_{r,c}` to :math:`M_{x,y}` then :code:`dim` should be the
   list :code:`[[r,x], [c,y]]`. If it maps :math:`M_m` to :math:`M_n`, then :code:`dim` can simply
   be the vector :code:`[m,n]`.

   More information can be found in Chapter: Unital Channels And Majorization from :cite:`Watrous_2018_TQI`).

   .. rubric:: Examples

   Consider the channel whose Choi matrix is the swap operator. This channel is an example of a
   unital channel.

   >>> from toqito.perms import swap_operator
   >>> from toqito.channel_props import is_unital
   >>>
   >>> choi = swap_operator(3)
   >>> is_unital(choi)
   True

   Additionally, the channel whose Choi matrix is the depolarizing channel is another example of
   a unital channel.

   >>> from toqito.channels import depolarizing
   >>> from toqito.channel_props import is_unital
   >>>
   >>> choi = depolarizing(4)
   >>> is_unital(choi)
   True

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param phi: The channel provided as either a Choi matrix or a list of Kraus operators.
   :param rtol: The relative tolerance parameter (default 1e-05).
   :param atol: The absolute tolerance parameter (default 1e-08).
   :param dim: A scalar, vector or matrix containing the input and output dimensions of PHI.
   :return: :code:`True` if the channel is unital, and :code:`False` otherwise.