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The thesis includes the original results of our articles [30, 37, 40, 42, 51,53, 75].  A method is developed to compute analytically entanglement measures ofthree-qubit pure states. Owing to it closed-form expressions are presented forthe geometric measure of entanglement for three-qubit states that are linearcombinations of four orthogonal product states. It turns out that the geometricmeasure for these states has three different expressions depending on the rangeof definition in parameter space and the Hilbert space of three-qubits consistsof three different entangled regions. The states that lie on joint surfacesseparating different entangled regions, designated as shared states, haveparticularly interesting features and are dual quantum channels for the perfectteleportation and superdense coding [42].  A powerful method is developed to compute analytically multipartiteentanglement measures. The method uses the duality concept and creates abijection between highly entangled quantum states and their nearest separablestates. The bijection gives explicitly the geometric entanglement measure ofarbitrary generalized W states of n qubits [30, 75]. Additionaly, the behaviorof the geometric entanglement measure of many-qubit W states is analyzed and aninterpolating formula is derived [51].  Generalized Schmidt decomposition of pure three-qubit states has fourpositive and one complex coefficients. In contrast to the bipartite case, theyare not arbitrary and the largest Schmidt coefficient restricts severely othercoefficients. It is derived a non-strict inequality between three-qubit Schmidtcoefficients, where the largest coefficient defines the least upper bound forthe three nondiagonal coefficients or, equivalently, the three nondiagonalcoefficients together define the greatest lower bound for the largestcoefficient [53].

Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems