Preparation of engineered multidimensional entangled states for optimal quantum information

Generation of maximally entangled states with different phase distributions and quantum states that can violate Bell's inequality stronger than a maximally entangled state are reported. The scheme can be used to enhance the efficiency of the quantum solution of a two- party communication complexity problem over any classical protocol by using two qutrit that violates Bell's inequality. Spatial amplitude profile of the pump beam that generates a maximally entangled qu-quart is given.