Theoretical Studies On Quantum State Teleportation, Assisted Cloning And Tomography

Many interesting applications have been found for the combination of quantum mechanics and information technology, i.e. in the field of quantum information and quantum computation, such as:quantum teleportation, assisted quantum cloning, quantum tomography, etc. Quantum state is the carrier of information, which plays a key role in quantum information and quantum computation. In the field of quantum mechanics, quantum state is not an observable. Quantum no-cloning theorem prohibits perfectly cloning an arbitrary unknown state. According to the uncertainty principle, quantum state may collapse in some certain state after measurement. In this dissertation, we focus on quantum state processing and proposed several quantum state processing protocols as follows:1. A tripartite scheme for probabilistically teleporting an arbitrary single-qubit state with 1D four-qubit cluster-type state as the quantum channel has been proposed. In the scheme, the sender and the controller both perform a Bell-state measurement on their respective qubit pair in their hands and announce the measurement results via classical communication. With the help of the sender and the controller, the receiver can reconstruct the original state with some probability by introducing an auxiliary qubit and making appropriate unitary operations and positive operator-valued measures (POVM). Moreover, the total success probability and classical communication cost of the present scheme are also calculated.2. A protocol for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance of a state preparer is presented. In this scheme, a genuine four-particle entangled state which can not be reduced to the product of two Bell states is used as the quantum channel. Moreover, POVM in stead of usual projective measurement is employed. In the assisted cloning protocol, the usual teleportation is required. And in the help of the state preparer, the perfect copies and complement copies of an unknown two-particle state can be implemented with a certain probability.3. Scheme for reconstructing an unknown two-particle mixed state by means of unambiguous state discrimination. In this protocol, an ancillary particle is introduced for distinguishing four nonorthogonal states. The discrimination process is performed by a bipartite unitary operation on the two-particle system and the ancilla followed by a von Neumann measurement (VNM) on the ancilla. Then the original two-particle system is measured in mutually unbiased bases. Consequently, the two-particle mixed state can be reconstructed. Furthermore, the total number of measurements in this protocol is less than that of the standard quantum tomography, thus the quantum resources is saved. Additionally, the nonorthogonal states discrimination and mutually unbiased measurement can be experimentally achieved, therefore our protocol may be realized with the current technology.4. Implementation of quantum state tomography scheme via discriminating two nonorthogonal quantum states in the linear optical system. In this scheme, to complete this discrimination process, we can resort to the optical system. By coupling one of the input state photons and an ancillary photon via beam splitter, a joint unitary transformation is performed. Then, we perform a von Neumann measurement on the ancillary particle in the standard basis. Thus, the nonorthogonal quantum states can be discriminated. Finally, we measure the original particle and the ancillary particle in the mutually unbiased bases. Therefore, any element of the matrix for the original quantum state can be reconstructed.