entanglement_fidelity

forest.benchmarking.distance_measures.entanglement_fidelity(pauli_lio0: numpy.ndarray, pauli_lio1: numpy.ndarray, tol: float = 1000) → float

Returns the entanglement fidelity (F_e) between two channels, E and F, represented as Pauli Liouville matrix.

The expression is

\[F_e(E,F) = Tr[E^\dagger F] / (dim^2),\]

where dim is the dimension of the Hilbert space associated with E and F.

See the following references for more information:

[GRAPTN] referenced in the superoperator_tools module. In particular section V subsection G.

[GFID]

A simple formula for the average gate fidelity of a quantum dynamical operation. M. Nielsen. Physics Letters A 303, 249 (2002). https://doi.org/10.1016/S0375-9601(02)01272-0 https://arxiv.org/abs/quant-ph/0205035

Parameters:

• pauli_lio0 – A dim**2 by dim**2 Pauli-Liouville matrix
• pauli_lio1 – A dim**2 by dim**2 Pauli-Liouville matrix
• tol – Tolerance in machine epsilons for np.real_if_close.

Returns:

Returns the entanglement fidelity between pauli_lio0 and pauli_lio1 which is a scalar.