Operation fidelity ($F_{\mathrm{op}}(\Lambda ,\rho )=\sqrt{F_e(\rho ,\Lambda )}$)

In the unsquared quantum fidelity convention, operation fidelity compares a purification of a density operator with its image under a quantum channel acting on the source subsystem:Its square is entanglement fidelity. Thus this convention is distinct from the squared quantity $F_e$; the two should not be installed as synonyms.

An operation fidelity used to compare a physically implemented quantum gate with its intended operation. A quantitative value requires a declared input-state average or another explicit channel-comparison convention; different conventions need not give the same number.