Some Studies On Quantum Cloning

Recent developments in quantum information and computation have given rise to an increasing number of applications, for instance, quantum teleportation, quan-tum dense coding, quantum cryptography, quantum logic gates, quantum algorithms and etc. These applications in quantum information processing (QIP) have different properties from the classical counterpart. Here, the basic theorem of the security of quantum cryptography is no-cloning theorem, which forbids cloning an unknown state perfectly. Since no-cloning theorem has a profound influence on quantum information, it becomes important to study quantum cloning machine (QCM). The author presents in detail some results on this topic. To be more specific,1. The Universal Quantum Cloning Machine (UQCM) and Phase-covariant Quan-tum Cloning Machine (PQCM) are two different types cloning machine which are used to copy quantum states with different inputs. The author studies out such general situation in which the states are distributed between to latitudes on a Bloch sphere. The result unifies the prior results pertaining to UQCM and PQCM:in particular, one could bring the two latitudes to the poles for UQCM or set the tow latitudes together for PQCM. It is generally believed that if one already has some prior information about the unknown state, he(she) can design a better copying machine for the state. Contrary to the general perception, the author points out that this view may not always true.2. It is well known that real physics systems are inevitably in a complicated en-vironment, which implies that real systems are always in a mixed state. Thus, it drives people to study the broadcasting of mixed states. The author presents an optimal 2→M phase-covariant quantum broadcasting of mixed equatorial qubits. This result shows that we can copy two identical mixed equatorial qubits with the same quantity as that of two identical pure equatorial states.3. The author studies the feasibility of implementing a quantum NOT gate (approx- imate) when the quantum state lies on two latitudes on the Bloch sphere and present an analytical formula for the optimized 1→M quantum NOT gate. The result generalizes previous results concerning quantum NOT gate for a quan-tum state distributed uniformly on the whole Bloch sphere as well as the phase-covariant quantum state. At the same time, the author points out that the 1→M optimal phase-covariant NOT gate can be replaced by combining the one to one perfect NOT gate and the 1→M PQCM.4. On the other hand, it is extremely different to generate experimentally multipar-tite entangled states through a single global unitary operation in general. For this purpose, the sequential generation of the entangled states appear to be promising and a lot of effort has been made in recent years. In this thesis, the author ana-lyzes the 1→M NOT gate within a sequential generation scheme and express the sequential quantum NOT gate in explicit form.