:py:mod:`channel_metrics.diamond_norm`
======================================

.. py:module:: channel_metrics.diamond_norm

.. autoapi-nested-parse::

   Compute the diamond norm between two quantum channels.



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


Functions
~~~~~~~~~

.. autoapisummary::

   channel_metrics.diamond_norm.diamond_norm



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

   Return the diamond norm distance between two quantum channels.

   The calculation uses the simplified semidefinite program of Watrous in
   :cite:`Watrous_2009_Semidefinite`.

   This function has been adapted from :cite:`Rigetti_2022_Forest`.

   .. 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:

   >>> import numpy as np
   >>> from toqito.channels import depolarizing
   >>> from toqito.channel_metrics import diamond_norm
   >>> choi_depolarizing = depolarizing(dim=2, param_p=0.2)
   >>> choi_identity = np.identity(2**2)
   >>> dn = diamond_norm(choi_depolarizing, choi_identity)
   >>> print("Diamond norm between depolarizing and identity channels: ", '%.2f' % dn)
   Diamond norm between depolarizing and identity channels:  -0.00

   .. note::
       You do not need to use `'%.2f' %` when you use this function.

       We use this to format our output such that `doctest` compares the calculated output to the
       expected output upto two decimal points only. The accuracy of the solvers can calculate the
       `float` output to a certain amount of precision such that the value deviates after a few digits
       of accuracy.

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

   >>> import numpy as np
   >>> from toqito.channels import dephasing
   >>> from toqito.channel_metrics import diamond_norm
   >>> choi_dephasing = dephasing(dim=2)
   >>> choi_identity = np.identity(2**2)
   >>> dn = diamond_norm(choi_dephasing, choi_identity)
   >>> print("Diamond norm between dephasing and identity channels: ", '%.2f' % dn)
   Diamond norm between dephasing and identity channels:  -0.00

   .. note::
       You do not need to use `'%.2f' %` when you use this function.

       We use this to format our output such that `doctest` compares the calculated output to the
       expected output upto two decimal points only. The accuracy of the solvers can calculate the
       `float` output to a certain amount of precision such that the value deviates after a few digits
       of accuracy.

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :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).