Quantum Squeezing And Entangling Power

We mainly consider two problems in this thesis. One is the relation between global squeezing character and local squeezing character in a composite system; the other is constructing quantum logic gate for qudit by using geometric phase and investigating its entangling power.We first introduce some basic concepts on squeezing state, and how to characterize spin squeezing or boson squeezing by using squeezing parameter. The squeezing property of a state is rooted in uncertainty relation, however, squeeze has a close relation with en-tanglement. For example, in a spin system, one can find that linear relation between spin squeezing parameter and concurrence which is used to characterize pairwise entanglement do exists. In this thesis we try to explain that there are two origins of quantum squeezing. We study the dynamical evolution of global and local quantum squeezing in both spin and boson composite system, and consider the squeezing properties for entangled spin coher-ent state and also entangled boson coherent state. We notice that both local squeezing and entanglement shared by the subsystems consist of the global squeezing for spin(j≥1) and boson composite systems. For the symmetric product state, global squeezing parameter would be equal to the local one. Thus we can assert that the difference between global and local squeezing parameter doesn't vanish is a sufficient criterion for the entanglement. We also find that the entanglement could enhance the global squeezing, at the meantime sup-press the local one. However, some kinds of entangled states would suppress both global and local squeezing.We then consider the entangling power of qudit geometric phase gate. Geometric phase gate is insensitive to the fluctuation of the environment. And qudit possess advan-tage while compare to the qubit. For example, quantum communication based on qudit would guarantee more security. We give the explicit form of qudit geometric phase gate. In quantum computation one would need quantum logic gate which can produce entangle-ment efficiently. The efficiency of a quantum gate is determined by its entangling power. For controlled-U gate, entangling power proportion to its operator entanglement. We study the 2-qudit geometric phase gate's operator entanglement and find that the qudit gate has more advantage than 2-qubit geometric phase gate.