toqito.channel_props.is_unitary
===============================

.. py:module:: toqito.channel_props.is_unitary

.. autoapi-nested-parse::

   Determines if a channel is unitary.





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

.. py:function:: is_unitary(phi)

   Given a quantum channel, determine if it is unitary.

   (Section 2.2.1: Definitions and Basic Notions Concerning Channels from
   [@Watrous_2018_TQI]).

   Let \(\mathcal{X}\) be a complex Euclidean space an let \(U \in U(\mathcal{X})\) be a
   unitary operator. Then a unitary channel is defined as:

   \[
       \Phi(X) = U X U^*.
   \]

   .. rubric:: Examples

   The identity channel is one example of a unitary channel:

   \[
       U =
       \begin{pmatrix}
           1 & 0 \\
           0 & 1
       \end{pmatrix}.
   \]

   We can verify this as follows:

   ```python exec="1" source="above"
   import numpy as np
   from toqito.channel_props import is_unitary

   kraus_ops = [[np.identity(2), np.identity(2)]]

   print(is_unitary(kraus_ops))
   ```

   We can also specify the input as a Choi matrix. For instance, consider the Choi matrix
   corresponding to the \(2\)-dimensional completely depolarizing channel.

   \[
       \Omega =
       \frac{1}{2}
       \begin{pmatrix}
           1 & 0 & 0 & 0 \\
           0 & 1 & 0 & 0 \\
           0 & 0 & 1 & 0 \\
           0 & 0 & 0 & 1
       \end{pmatrix}.
   \]

   We may verify that this channel is not a unitary channel.

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

   print(is_unitary(depolarizing(2)))
   ```

   :param phi: The channel provided as either a Choi matrix or a list of Kraus operators.

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