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qiskit.quantum_info.state_fidelity

state_fidelity(state1, state2, validate=True)[source]

Return the state fidelity between two quantum states.

The state fidelity \(F\) for density matrix input states \(\rho_1, \rho_2\) is given by

\[F(\rho_1, \rho_2) = Tr[\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}}]^2.\]

If one of the states is a pure state this simplies to \(F(\rho_1, \rho_2) = \langle\psi_1|\rho_2|\psi_1\rangle\), where \(\rho_1 = |\psi_1\rangle\!\langle\psi_1|\).

Parameters
Returns

The state fidelity \(F(\rho_1, \rho_2)\).

Return type

float

Raises

QiskitError – if validate=True and the inputs are invalid quantum states.

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