toqito.channel_metrics.completely_bounded_trace_norm

Computes the completely bounded trace norm of a quantum channel.

Module Contents

toqito.channel_metrics.completely_bounded_trace_norm.completely_bounded_trace_norm(phi, solver='cvxopt', **kwargs)[source]

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.

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.

Parameters:

  • phi (numpy.ndarray) – superoperator as choi matrix

  • solver (str) – Optimization option for picos solver. Default option is solver=”cvxopt”.

  • kwargs – Additional arguments to pass to picos’ solve method.

Returns:

The completely bounded trace norm of the channel

Return type:

float | numpy.floating