toqito.channel_metrics.completely_bounded_trace_norm
====================================================

.. py:module:: toqito.channel_metrics.completely_bounded_trace_norm

.. autoapi-nested-parse::

   Computes the completely bounded trace norm of a quantum channel.





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

.. py:function:: completely_bounded_trace_norm(phi, solver = 'cvxopt', **kwargs)

   Find the completely bounded trace norm of a quantum channel.

   Also known as the diamond norm of a quantum channel (Section 3.3.2 of [@Watrous_2018_TQI]). The algorithm in p.11 of
   [@Watrous_2012_Simpler] with implementation in QETLAB [@QETLAB_link] is used.

   .. rubric:: Examples

   To compute the completely bounded trace norm of a depolarizing channel:

   ```python exec="1" source="above"
   from toqito.channels import depolarizing
   from toqito.channel_metrics import completely_bounded_trace_norm
   # Define the depolarizing channel
   choi_depolarizing = depolarizing(dim=2, param_p=0.2)
   print(completely_bounded_trace_norm(choi_depolarizing))
   ```

   :raises ValueError: If matrix is not square.

   :param phi: superoperator as choi matrix
   :param solver: Optimization option for `picos` solver. Default option is `solver="cvxopt"`.
   :param kwargs: Additional arguments to pass to picos' solve method.

   :returns: The completely bounded trace norm of the channel