channel_metrics.completely_bounded_trace_norm

Computes the completely bounded trace norm of a quantum channel.

Functions

completely_bounded_trace_norm(phi[, solver])

Find the completely bounded trace norm of a quantum channel.

Module Contents

channel_metrics.completely_bounded_trace_norm.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 [1]). The algorithm in p.11 of [2] with implementation in QETLAB [3] is used.

Examples

To computer the completely bounded spectral norm of a depolarizing channel,

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)
completely_bounded_trace_norm(choi_depolarizing)

1

References

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