channel_metrics.diamond_distance
================================

.. py:module:: channel_metrics.diamond_distance

.. autoapi-nested-parse::

   Computes the diamond norm between two quantum channels.



Functions
---------

.. autoapisummary::

   channel_metrics.diamond_distance.diamond_distance


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

.. py:function:: diamond_distance(choi_1, choi_2)

   Return the diamond norm distance between two quantum channels.

   This function is a wrapper around :func:`.completely_bounded_trace_norm`,
   in that it returns half of the completely bounded trace norm of the difference of its arguments.

   .. note::
       This calculation becomes very slow for 4 or more qubits.


   .. rubric:: Examples

   Consider the depolarizing and identity channels in a 2-dimensional space. The depolarizing channel parameter is
   set to 0.2:

   .. jupyter-execute::

       import numpy as np
       from toqito.channels import depolarizing
       from toqito.channel_metrics import diamond_distance
       choi_depolarizing = depolarizing(dim=2, param_p=0.2)
       choi_identity = np.identity(2**2)
       diamond_distance(choi_depolarizing, choi_identity)

   Similarly, we can compute the diamond norm between the dephasing channel (with parameter 0.3) and the identity
   channel:

   .. jupyter-execute::

       import numpy as np
       from toqito.channels import dephasing
       from toqito.channel_metrics import diamond_distance
       choi_dephasing = dephasing(dim=2)
       choi_identity = np.identity(2**2)
       diamond_distance(choi_dephasing, choi_identity)


   .. rubric:: References

   .. footbibliography::

   :raises ValueError: If matrices are not of equal dimension.
   :raises ValueError: If matrices are not square.
   :param choi_1: A 4**N by 4**N matrix (where N is the number of qubits).
   :param choi_2: A 4**N by 4**N matrix (where N is the number of qubits).