  The notion of entanglement fidelity is to measure entanglement preservation
through quantum channels. Nevertheless, the amount of entanglement present in a
state of a quantum system at any time is measured by quantities known as
measures of entanglement. Since there are different types of measures of
entanglement, one may expect an entanglement fidelity to associate with its own
measure of entanglement counterpart. Here, we aim to investigate association
between the so called entanglement fidelity and some measures of entanglement,
namely, entanglement of formation, concurrence and negativity. New entanglement
fidelities based upon these measures of entanglement are introduced and
statistically compared with the so called previously introduced entanglement
fidelity. It is shown that the entangling aspect of the so called entanglement
fidelity is neither of type entanglement of formation and concurrence nor of
type negativity. The results, in addition, expose inability of the so called
entanglement fidelity for detecting, in a broad sense, entanglement
preservation through quantum channels. Our analyses opens up a new venue in the
study of entanglement fidelity and measure of entanglement by demonstrating
that each measure of entanglement solely defines its own entanglement fidelity.
