  For a given ensemble of input and target states, the classical fidelity
threshold (CFT) is the maximum valve of the averaged fidelity, and it can be
achieved with a measure-and-prepare operation. This quantity can be employed to
verify whether the channel is in the quantum domain or not. In a recent work by
Chiribella and Xie [Phys. Rev. Lett. {\bf 110}, 213601 (2013)], it was showed
that all the information about the input and target states can be equivalently
described by an entangled state and an effective entanglement-braking (EB)
channel, and the CFTs can be defined with the Choi matrix of the effective EB
channel. Following this idea, the protocol proposed by Fuchs and Sasaki
[Quantum. Inf. Comput, {\bf 3}, 377 (2003)] are reformulated in terms of the
effective EB channel, and ss applications, the deterministic and probabilistic
CFTs for qubit states and the coherent states are derived in this paper.
