  The wedge product of vectors has been shown to yield the generalised
entanglement measure I-concurrence, wherein the separability of the multiparty
qubit system arises from the parallelism of vectors in the underlying Hilbert
space of the subsystems. Here, we demonstrate the geometrical conditions of the
post-measurement vectors which maximize the entanglement corresponding to the
bi-partitions and can yield non-identical set of maximally entangled states.
The Bell states for the two qubit case, GHZ and GHZ like states with
superposition of four constituents for three qubits, naturally arise as the
maximally entangled states. The geometric conditions for maximally entangled
two qudit systems are derived, leading to the generalised Bell states, where
the reduced density matrices are maximally mixed. We further show that the
reduced density matrix for an arbitrary finite dimensional subsystem of a
general qudit state can be constructed from the overlap of the post-measurement
vectors. Using this approach, we discuss the trade-off between the local
properties namely predictability and coherence with the global property,
entanglement for the non-maximally entangled two qubit state.
