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state_fidelity(state1, state2, validate=True)

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Return the state fidelity between two quantum states.

The state fidelity FF for density matrix input states ρ1,ρ2\rho_1, \rho_2 is given by

F(ρ1,ρ2)=Tr[ρ1ρ2ρ1]2.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 simplifies to F(ρ1,ρ2)=ψ1ρ2ψ1F(\rho_1, \rho_2) = \langle\psi_1|\rho_2|\psi_1\rangle, where ρ1=ψ1 ⁣ψ1\rho_1 = |\psi_1\rangle\!\langle\psi_1|.



The state fidelity F(ρ1,ρ2)F(\rho_1, \rho_2).

Return type



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

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