Researches Of Several Quantum Characters In Quantum Time Evolution Process

Several quantum characters and quantum effects manifest during quantum evolu-tion process, among these features, we focus on the following directions:Geometric phase(GP), Time-optimal quantum evolution, The capacity of generating quantum cor-relations of a non-local unitary operator.First. We combine these two different directions——GP and time-optimal quan-tum evolution——by considering the problem straightforwardly in projective Hilbert space. Through the research of key concepts such as Geodesics and Null Phase Curves we provide their relationship and show that these two different directions have the same theoretical basis.Second. Quantum correlations, which is generated by non-local unitary operators in quantum mechanics, is regarded as the essential reason why quantum theory can pro-vide better results than corresponding classical cases in many application areas such as quantum information and computation. Available researches are mainly focused on the entangling capacity of unitary operators that acting on pure initial state, here we con-sider some typical kinds of unitaries acting on certain mixed initial states and compare the quantum entanglement generated by the operators. The result shows that pure input states driven by some unitary transformation may become maximum entangled states, however, it is not the case for mixed input state.Third. Quantum discord, which was first proposed by Ollivier and Zurek, is a new measurement of quantum correlation, so far, quantum discord has been calculated ex-plicitly only for a rather limited set of two-qubit quantum states called X-state. Here we provide a geometric description of quantum discord based on the conception of quantum steering ellipsoid and derive analytical expressions of quantum discord for all two-qubit rank-two states. We further discuss the ability of generating quantum discord of differ-ent quantum gates.