toqito.channel_props.is_quantum_channel
=======================================

.. py:module:: toqito.channel_props.is_quantum_channel

.. autoapi-nested-parse::

   Determines if an input is a quantum channel.





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

.. py:function:: is_quantum_channel(phi, rtol = 1e-05, atol = 1e-08)

   Determine whether the given input is a quantum channel.

   For more info, see Section 2.2.1: Definitions and Basic Notions Concerning Channels from
   [@Watrous_2018_TQI].

   A map \(\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)\) is a *quantum
   channel* for some choice of complex Euclidean spaces \(\mathcal{X}\)
   and \(\mathcal{Y}\), if it holds that:

   1. \(\Phi\) is completely positive.
   2. \(\Phi\) is trace preserving.

   .. rubric:: Examples

   We can specify the input as a list of Kraus operators. Consider the map \(\Phi\) defined as

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

   where

   \[
       U = \frac{1}{\sqrt{2}}
       \begin{pmatrix}
           1 & 1 \\
           -1 & 1
       \end{pmatrix}.
   \]

   To check if this is a valid quantum channel or not,

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

   U = (1/np.sqrt(2))*np.array([[1, 1],[-1, 1]])
   X = pauli("X")
   phi = X - np.matmul(U, np.matmul(X, np.conjugate(U)))

   print(is_quantum_channel(phi))
   ```

   If we instead check for the validity of depolarizing channel being a valid quantum channel,

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

   choi_depolarizing = depolarizing(dim=2, param_p=0.2)

   print(is_quantum_channel(choi_depolarizing))
   ```

   :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).

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