Source code for toqito.channel_metrics.diamond_distance

"""Computes the diamond norm between two quantum channels."""

import numpy as np




def diamond_distance(choi_1: np.ndarray, choi_2: np.ndarray) -> float | np.floating:
    r"""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.

    Args:
        choi_1: A 4**N by 4**N matrix (where N is the number of qubits).
        choi_2: A 4**N by 4**N matrix (where N is the number of qubits).

    """
    from toqito.channel_metrics import completely_bounded_trace_norm  # noqa

    return completely_bounded_trace_norm(choi_1 - choi_2)