  Groverian and Geometric entanglement measures of the n-party pure state are
expressed by the (n-1)-party reduced state density operator directly. This main
theorem derives several important consequences. First, if two pure n-qudit
states have reduced states of (n-1)-qudits, which are equivalent under local
unitary(LU) transformations, then they have equal Groverian and Geometric
entanglement measures. Second, both measures have an upper bound for pure
states. However, this upper bound is reached only for two qubit systems. Third,
it converts effectively the nonlinear eigenvalue problem for three qubit
Groverian measure into linear eigenvalue equations. Some typical solutions of
these linear equations are written explicitly and the features of the general
solution are discussed in detail.
