toqito.channel_props.is_unital
==============================

.. py:module:: toqito.channel_props.is_unital

.. autoapi-nested-parse::

   Determines if a channel is unital.





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

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

   Determine whether the given channel is unital.

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

   \[
       \Phi(\mathbb{I}_{\mathcal{X}}) = \mathbb{I}_{\mathcal{Y}}.
   \]

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

   More information can be found in Chapter: Unital Channels And Majorization from [@Watrous_2018_TQI]).

   .. rubric:: Examples

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

   ```python exec="1" source="above"
   from toqito.perms import swap_operator
   from toqito.channel_props import is_unital

   choi = swap_operator(3)

   print(is_unital(choi))
   ```

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

   ```python exec="1" source="above"
   from toqito.channels import depolarizing
   from toqito.channel_props import is_unital

   choi = depolarizing(4)

   print(is_unital(choi))
   ```

   :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.

   :returns: `True` if the channel is unital, and `False` otherwise.