fidelity

forest.benchmarking.distance_measures.fidelity(rho: numpy.ndarray, sigma: numpy.ndarray, tol: float = 1000) → float

Computes the fidelity \(F(\rho, \sigma)\) between two quantum states rho and sigma.

If the states are pure the expression reduces to

\[F(|psi>,|phi>) = |<psi|phi>|^2\]

The fidelity obeys \(0 ≤ F(\rho, \sigma) ≤ 1\), where \(F(\rho, \sigma)=1 iff \rho = \sigma\).

Parameters:

• rho – Is a dim by dim positive matrix with unit trace.
• sigma – Is a dim by dim positive matrix with unit trace.
• tol – Tolerance in machine epsilons for np.real_if_close.

Returns:

Fidelity which is a scalar.