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

Geometric quantification of multiparty entanglement through orthogonality of vectors