Certain Problems On Universal Quantum Cloning Machines And Adiabatic Implementation

The thesis combined our researches on Quantum theory and quantum informationtheory in past few years. The main content of this paper contains :First, we propose a single Hermitian operator, whose maximum eigenvalue givesthe optimal fidelity of the universal symmetric cloning machines and the correspondingeigenspace can be used to define the cloning transformations. Possibility of implementinguniversal quantum cloning machines via adiabatic evolution is also discussed.Second, The trade-o?s among various output fidelities of asymmetric universal cloningmachines are investigated. Firstly we find out all the attainable optimal output fidelitiesfor the 1 to 3 asymmetric universal cloning machine and it turns out that there are twokinds of extremal machines which have to cooperate in order to achieve some of the opti-mal output fidelities. Secondly we construct a family of extremal cloning machines thatincludes the universal symmetric cloning machine as well as an asymmetric 1 to 1 + Ncloning machine for qudits with two di?erent output fidelities such that the optimal trade-o? between the measurement disturbance and state estimation is attained in the limit ofinfinite N.Third, based on the idea of quantum adiabatic theorem and asymmetric universalcloning machines, we propose an adiabatic realization of the asymmetric cloning machinevia a 3-particle XXY chain bathed in a transverse magnetic field by adiabatically turningo? the transverse magnetic field and turning on the two-body interactions among threeparticles. It turns out that a phase operation that depends on the output fidelities isrealized simultaneously.