Quantum Decoherence Studied By Using Entangled State Representation

Decoherence is a universal essential problem in modern quantum information and quan-tum computation. It is significant and difficult to study this problem in modern physical field.Its difficulty is from the absent of an effective theory to deal with decoherence of quantumstate with continuum variables. Although there is a super-operator method, it has much in-sufficiency. In this thesis, we propose a new theory to deal with quantum decoherence, i.e.,by introducing a thermo entangled state representation. Our method is not only convenientand effective, but also can enrich and develop the sum-representation theory of Kraus opera-tor. The reasons are that, on one hand, the IWOP technique generalizes the Newton-Leibnizrule to the integrations over the operators in quantum mechanics, which is usually not com-mutative, thus it creates a bridge between classical mechanics and quantum mechanics; onthe other hand, the thermo entangled state representation itself exhibits the entanglement be-tween quantum system and environment so that the essence of decoherence can be open outdirectly by using this new representation. The special merits are (1) converting convenientlythe master equation (ME) of density operator to c-number equation; (2) solving analyticallyMS and obtaining the Kraus operator sum representation of density operator; (3) provingeffectively the normalization of Kraus operator by using the IWOP technique; (4) derivingthe time evolution of Wigner function and photon distribution in a concise process. Thus ourtheory may be adapted extensively. Our main contents are as follows:一. Based on the IWOP technique and the thermo dynamics theory, we introduce a newthermo entangled state representation with continuous variables to study the decoherence ofopen quantum system. By using |η>, one can convert conveniently the master equationof density operatorρinto c-number (differential) equation about function <η|ρ>, whichis more concise than that in traditional form. For solving <η|ρ>, we have also set upthe relation between the thermo entangled state representation and Wigner function, densityoperator and positive P-representation, and vice versa. In addition, using <η|ρ> we put thecalculation for any operator's average value in density operator into a matrix element in theframe of thermo dynamics theory, which is more convenient. 二. Using |η>, we further have analytically solved some familiar MEs of quantum op-tical systems, such as amplitude damping, (generalized) phase diffusion, squeezing sensitivereservoirs, laser theory in the lowest-order approximation (involving ME at finite tempera-ture), amplitude damping with a Kerr medium and parametric down conversion. For the firsttime, we have derived the infinite sum representation of density operators and proved the nor-malization of Kraus operators by virtue of the IWOP technique. These results can provide uswith an intuitionistic way to grasp the essence of decoherence (quantum entanglement), butwith conveniences for solving other decoherence models. In addition, we have generalizedthe discrete sum representation of density operators to the continuum sum representation inquantum teleportation. This further develops the Kraus operator sum representation form thediscrete finite sum case to the discrete infinite sum case, then to the continuum sum case.三.Employing the antinormal ordering form of product of operators and Weyl repre-sentation, we have derived two new photon-count formulas, which are related to Wignerfunction and Q-representation of density operator, respectively. Further, for some decoher-ence models, we have derived the evolution formula of Wigner function by using |η> andseveral new formulas of photon distribution from the relation between photon distributionand Wigner function. These formulas will provide us with convenience for studying thenonclassicality of quantum system.四.By virtue of the IWOP technique and these method above, we have discussed fullyand analytically the evolution of some classical quantum states (photon-added coherent state,single-mode and two-mode photon-subtracted squeezed state) in environment, such as nor-malization factor, Wigner function, Husimi function, photon distribution and quantum to-mography. These analytical results can help us to not only understand clearly the dissipativereservoir's effect to quantum state, but also provide a valuable reference for the experimentaltest.