channel_metrics.completely_bounded_trace_norm

Computes the completely bounded trace norm of a quantum channel.

Functions

completely_bounded_trace_norm(phi)

Find the completely bounded trace norm of a quantum channel.

Module Contents

channel_metrics.completely_bounded_trace_norm.completely_bounded_trace_norm(phi)

Find the completely bounded trace norm of a quantum channel.

Also known as the completely bounded diamond norm of a quantum channel (Section 3.3.2 of [1]). The algorithm in p.11 of [3] with implementation in QETLAB [1] 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

[1]

John Watrous. The Theory of Quantum Information. Cambridge University Press, 2018. URL: https://johnwatrous.com/wp-content/uploads/TQI.pdf, doi:10.1017/9781316848142.

[2]

Nathaniel Johnston. QETLAB: A MATLAB toolbox for quantum entanglement. URL: https://github.com/nathanieljohnston/QETLAB, doi:10.5281/zenodo.44637.

[3]

John Watrous. Simpler semidefinite programs for completely bounded norms. 2012. arXiv:1207.5726.

Raises:

ValueError – If matrix is not square.

Parameters:

phi (numpy.ndarray) – superoperator as choi matrix

Returns:

The completely bounded trace norm of the channel

Return type:

float