Is 2-EPP good at low rates for a phase-damping channel ?

Recently, we demonstrated that a 2-EPP is superior to a 1-EPP if fifteen entangled states are initially shared via a phase-damping channel. We seek to prove that 2-EPP is superior to 1-EPPs when there is only one kind of error. In the present paper, we show property of exponential bounds on fidelity of EPPs, which correspond to bounds on error exponent in usual information transmission. As a result, an exponential bound for the fidelity of a particular 2-EPP is always higher than that of 1-EPPs, at least at low rates if the channel is assumed to be phase damped.