  One of the biggest problems in the theory of quantum information is the
quantification of amount of entanglement in an arbitrary multipartite mixed
state. Different axiomatic and operational measures were proposed so far. In
this work we will establish a connection between geometric measure of
entanglement proposed in [Phys. Rev. A 68, 042307 (2003)] and measures based on
fidelity. One result will be, that geometric and revised geometric measure of
entanglement proposed in [J. Phys. A: Math. Theor. 40, 3507 (2007)] are equal.
Further a useful expression for fidelity is derived.
