Entropy And Entanglement In The Quantum System

Entropy and entanglement in the quantum systemWang Cheng-Zhi Directed by professor Fang Mao-Fa .Department of Physics, Hunan Normal University, Changsha, 410081, ChinaRecently, considerable attention has been paid to the application of quantum entropy theory in quantum physics, specially, in quantum optics and quantum information. Quantum entropy theory is the foundation and powerful tool in understanding and studying such problems as quantum computation, quantum communication, quantum teleportation, quantum measurement and quantum entanglement. The squeezing of the field and atom intensively studied due to its practical application, the reference[16] presented the squeezing theory of quantum information for a high sensitive measurement of the squeezing effects of the field and atom.In this thesis, quantum entropy theories are applied to study quantum entanglement and other problems: quantum channel ?two-particle teleportation and its interpretation in terms of entropy ?quantum information squeezing of atom and so on in quantum systems. The thesis is structured as follows:In the first chapter, quantum entropy basal conception and related theories are concisely introduced. In the chapter 2,4 and 5, the entropic dynamics and the properties of entanglement are investigated in quantum system.' In the 2 of these chapters, the decoherence and entanglement of the two-mode squeezing vacuum state are studied under the influence of the special environment (atom). Notonly the quantum entanglement between the atom and two-mode squeezing vacuum state is studied, but also the quantum entanglement between two modes of the two-mode light field state is studied. By the studying of quantum entanglement between two modes of the two-mode light field state and fidelity of the two-mode light field state, we find that, if the initial conditions of the system are properly selected, the two-mode squeezing vacuum state used in quantum communication still keeps high degree of entanglement during the interaction between atom and light field, which is significative to quantum communication; In the chapter 4, quantum entanglement in a two-dimensional ion trap is investigated. In this chapter, the model of between two leasers and a trapped ion is presented. The entanglement between two degrees of freedom is initially investigated by using quantum relative entropy, in addition to the entanglement between two degrees of freedom(ion and phonon). The findings give that entanglement between two degrees of freedom of the phonon varies with time, although there is no interaction between the two degrees of freedom, and the relation between the two entanglements is discovered for the first time. Moreover, the findings also shows that system initial state entanglement has vast influence on the two entangiements;In chapter 5, the influence of nolinear interaction on entanglement and the relation between atomic collapse-revive and entanglement are discussed in two-mode nolinear J-C model. The first result gives that when the Kerr medium does not exist, the findings is the same as these in the chapter 4, but when the Kerr medium exists, evolutions of entanglements are periodic, another new result is that time when atom is collapsing and reviving corresponds to the special entanglement. Ohya mutual entropic theory is introduced into the study on the two-photon process of atom and two-mode squeezing vacuum state in chapter 3. The expression of atomic mutual entropy is derived. Periodicity of. the quantum mechanical channel is displayed , and the influence of squeezing coefficient on atomic mutual entropy is investigated; chapter 6 gives a scheme for realizing the squeezingof atomic information entropy is brought forward . This scheme is easily experimentally performed and is a effective avenue to realize the atomic squeezing; In chapter 7, a scheme for quantum teleportation of two-particle arbitrary pure two-levelstates is proposed, whose interpretation in terms of quantum information is given by using quantum entropy t...