channel_metrics.diamond_distance

Computes the diamond norm between two quantum channels.

Functions

diamond_distance(choi_1, choi_2)

Return the diamond norm distance between two quantum channels.

Module Contents

channel_metrics.diamond_distance.diamond_distance(choi_1, choi_2)

Return the diamond norm distance between two quantum channels.

This function is a wrapper around 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:

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)
diamond_distance(choi_depolarizing, choi_identity)

1.0000000000261728

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

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)
diamond_distance(choi_dephasing, choi_identity)

1.0000000000273863

References

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