iqm.benchmarks.compressive_gst.mgst.low_level_jit.Mp_norm_lower

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iqm.benchmarks.compressive_gst.mgst.low_level_jit.Mp_norm_lower#

iqm.benchmarks.compressive_gst.mgst.low_level_jit.Mp_norm_lower(X_true: ndarray, E_true: ndarray, rho_true: ndarray, X: ndarray, E: ndarray, rho: ndarray, J: ndarray, p: float) → tuple[float, float]#

Compute the Mp-norm lower bound of the distance between true and estimated parameters.

This function calculates the lower bound of the Mp-norm between the true parameters (X_true, E_true, rho_true) and the estimated parameters (X, E, rho) based on the provided J indices.

Parameters:

  • X_true (ndarray) – A 3D array containing true input matrices, of shape (n_matrices, n_rows, n_columns).

  • E_true (ndarray) – A 2D array representing the true POVM elements, of shape (n_povm, r).

  • rho_true (ndarray) – A 1D array representing the true density matrix.

  • X (ndarray) – A 3D array containing estimated input matrices, of shape (n_matrices, n_rows, n_columns).

  • E (ndarray) – A 2D array representing the estimated POVM elements, of shape (n_povm, r).

  • rho (ndarray) – A 1D array representing the estimated density matrix.

  • J (ndarray) – A 2D array representing indices for which the objective function will be evaluated.

  • p (float) – The order of the Mp-norm (p > 0).

Returns:

A tuple containing the Mp-norm lower bound and the maximum distance.

Return type:

tuple[float, float]

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