Ket-Bra Entangled State Method In Open Quantum System

At the end of the 20th century, the collision and combination between Quantum Mechanics and Information Theory had hasten a new inter-discipline-Quantum Infor-mation Theory, which had mostly drawn the attention of physicist due to its intrinsic physical significance and its potential applications. Quantum coherence and quantum entanglement both of which play a crucial role in the field such as quantum commu-nication, quantum control, quantum teleportation and quantum computing, these quan-tum characteristics can be viewed as a resource that allows unique application in the corresponding field of quantum information. However, the real quantum system is u-navoidable coupled with the environment, which shall lead to a loss of coherence and entanglement, these process are called decoherence and disentanglement which is the chief obstacle to the realization of quantum communication and quantum computer.Generally, the evolution of isolated and closed system should be unitary according to the Schrodinger equation. It’s impossible for any quantum system to totally isolate from environment except the whole universe, thus there always are some interaction be-tween the system and environment which lead to the decoherence and disentanglement of the open quantum system; While most quantum information process include quan-tum computing and quantum teleportation that crucial rely on the unitary operations of the system, but the decoherence may break the unitary evolution of the system, thus it shall introduce more errors into the quantum information process.To overcome the decoherence and realize quantum information technology, much effort has been maked to investigate the dynamic evolution of open quantum system. The open quantum system consist of system and environment, the evlution of the whole was governed by the Heisenberg equation and the dynamic equation of system can be deduced by partial trace of the environment, the dynamic equation of system is the so-called quantum master equation. The quantum master equation is a linear differential equation of different operators in the view of mathematics. Many method have been introduced to solve the master equation, which can be divided into two categories-C-number method and Super-Operator method; However both methods have some de-merits, for instance, C-number method can convert master equation into the general F-P equation but it’s quite difficult for some equation and the solution is not always applicable for any initial state, while the super-operator method rely on the Lie algebra structure of master equation thus it has a narrow applicable range.To overcome the demerits of C-number method and super-operator method, we introduce a new Ket-Bra Entangled State(KBES) method which enable one to convert master equation into Schrodinger-like equation. Compared with C-number method and super-operator method, There are several merits of ket-bra entangled state method:1. Ket-Bra entangled method have more widely applicable range, it’s applicable for any master equation of finite-level system in theory, while the super-operator method rely on the Lie algebra structure of master equation and even slightly change to the master equation may lead to the failure of super-operator method.2. Ket-Bra entangled method is more concise, and the solution is applicable for any initial state; Besides, the procedure is easily programmed and the calculation can be fully finished by compuer.3. Ket-Bra entangled method enables one convert master equation into Schrodinger-like equation, thus the mature method can be used to solve master equation. For instance, all of evolution operator method, perturbation method and station-ary Schrodinger equation method may be used to solve master equation through KBES method.Finally, we utlize this Ket-Bra entangled state method to solve the master equation of finite-level systems include a two-level damped atom under the time-varying external field, a damped V-type qutrit,2-qubit X X Z open spin chain and N-Qubit X X Z open spin chain. Then we research the dynamic evolution of entanglement and coherence of such system which exhibit that the interplay between the subsystem shall lead to the entanglement sudden death phenomenon and entanglement sudden birth phenomenon. The interplay between subsystem contribute to supress the decoherence and disentan-glement, especially for the case of 2-Qubit open sipn chain which still keep entanged even for tâ†'∞. The research of damped two-level qubit under time-varying external field show that the entanglement sudden birth still exist even without the interaction between subsystem and the non-Markov environment, this imply that maybe we can control the decoherence by applying external field on the system. All of our research signify that the control of decoherence is possible by the interplay between subsystem and applying external field on the system.