smith_fidelity

forest.benchmarking.distance_measures.smith_fidelity(rho: numpy.ndarray, sigma: numpy.ndarray, power) → float

Computes the Smith fidelity \(F_S(\rho, \sigma, power)\) between two quantum states rho and sigma.

The Smith fidelity is defined as \(F_S = \sqrt{F^{power}}\), where F is standard fidelity \(F = fidelity(\rho, \sigma)\). Since the power is only defined for values less than 2, it is always true that \(F_S > F\).

At present there is no known operational interpretation of the Smith fidelity for an arbitrary power.

Parameters:

• rho – Is a dim by dim positive matrix with unit trace.
• sigma – Is a dim by dim positive matrix with unit trace.
• power – Is a positive scalar less than 2.

Returns:

Smith Fidelity which is a scalar.