Quantum Entanglement In Open Systems And Research On (?) Ordering Problems Of Quantum Operators

Quantum entanglement is an important feature of quantum physics different from classical physics, which embodies the nonlocality of quantum mechanics and plays a vital role in quantum information processing and quantum communication. By means of quantum entanglement one can achieve some tasks which can not be realized via classical methods, such as quantum teleportation, quantum dense coding, quantum error correcting and quantum computation, and so on. However, any real physical carrier in which entanglement is stored would unavoidably interact with external environment and cause local decoherence, which would eventually destroy the necessary entanglement of the whole quantum system and even cause entanglement sudder death. So studying entanglement dynamics in open system will be useful for better exploring, protecting and controlling entanglement.In quantum physics, observable quantities are represented by operators which are not commutable in most cases, for example the coordinate and momentum operators have commutation relation ? ?[Q, P] ?i(??1). So operator’s ordering problem is often concerned. In fact, the operator’s normal ordering, antinormal ordering and Weyl ordering have provided conveniences in solving actual physics problems. The people should further research operator’s ordering problem, which can help solve actual problem and understand quantum physics law.In this paper, we mainly research the dynamics of quantum entanglement in open environment and Q-P ordering of quantum operators. The main results of this thesis are as follows:1. Considering six two-level atoms interacting with three independent reservoirs, their entanglement dynamics are studied. The influences of environment, atoms’ initial state and the relative coupling strength on tripartite entanglement are analyzed.2.We study the dynamics of three entangled two-level atoms in a common reservoir or three independent reservoirs. Weak measurement and quantum measurement reversal are performed before and after experiencing decoherence environment. The results show quantum entanglement can be improved obviously and be affected by measurement strength, initial entanglement and external environment.3. In the case of considering the DM interaction between the two lattices, we investigate the thermal entanglement in the two-qubit Ising model in an inhomogeneous magnetic field. We analyze the influence of the external magnetic, DM interaction and temperature on the thermal entanglement, and prove the relation between quantum phase transition and thermal entanglement.4. We deduce the Q- and P ordered differentiation form of the Wigner operator and study the Weyl prescription and its inverse transform which makes mutual transformation between classical function and quantum operators realizable by means of differential operation. The method of transforming any operator function into Q-P ordering is also given. Furthermore, we find a general Wigner operaor expressed by differential form, which can unify Weyl ordering, Q ordering and P ordering.