toqito.channel_metrics.diamond_distance

Computes the diamond norm between two quantum channels.

Module Contents

toqito.channel_metrics.diamond_distance.diamond_distance(choi_1, choi_2)[source]

Return the diamond norm distance between two quantum channels.

This function is a wrapper around [completely_bounded_trace_norm] [toqito.channel_metrics.completely_bounded_trace_norm.completely_bounded_trace_norm], in that it returns half of the completely bounded trace norm of the difference of its arguments.

!!! note

This calculation becomes very slow for 4 or more qubits.

Examples

Consider the depolarizing and identity channels in a 2-dimensional space. The depolarizing channel parameter is set to 0.2:

`python exec="1" source="above" import numpy as np from toqito.channels import depolarizing from toqito.channel_metrics import diamond_distance choi_depolarizing = depolarizing(dim=2, param_p=0.2) choi_identity = np.identity(2**2) print(diamond_distance(choi_depolarizing, choi_identity)) `

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

`python exec="1" source="above" import numpy as np from toqito.channels import dephasing from toqito.channel_metrics import diamond_distance choi_dephasing = dephasing(dim=2) choi_identity = np.identity(2**2) print(diamond_distance(choi_dephasing, choi_identity)) `

Raises:

  • ValueError – If matrices are not of equal dimension.

  • ValueError – If matrices are not square.

Parameters:

  • choi_1 (numpy.ndarray) – A 4**N by 4**N matrix (where N is the number of qubits).

  • choi_2 (numpy.ndarray) – A 4**N by 4**N matrix (where N is the number of qubits).

Return type:

float | numpy.floating