Remote State Preparation And Entangled State Analysis

Quantum information is a new interdisciplinary developed in recent thirty years. It involves a number of scientific researches in the field of physics, information science, cryptography, mathematics and so on. Quantum information mainly contains two branches, quantum computation and quantum communication, both of which consider quantum state as the information carrier and utilize the basic quantum mechanics principles to achieve the computing power and security that cannot be realized by classical computation and communication. Quantum entanglement is a unique phenomenon in the quantum world, without classical counterpart. It is also an important resource, which is widely used in quantum information processing.There are four parts of information processing, i.e., the initialization, transmission, manipulation and read-out, corresponding to the preparation, transmission, manipulation and measurement of the quantum state in practical experiment. Transmission of a state which carries the secret information is essential in quantum information processing. The most intuitive way is transmitting directly via practical channel. However, in this case the state will be exposed to potential eavesdroppers and environmental noise, which will affect the security and success probability of the entire communication scheme. The basic principles of quantum mechanics provide us a safer and more effective way to transmit information, which is to establish entanglement channel, then realize the non-direct transmission. Two typical quantum non-direct transmission methods are quantum teleportation and remote state preparation, respectively.In this thesis, we propose two controlled remote state preparation protocols via partially entangled channels. One prepares a single-qubit state, and the other prepares a two-qubit state. Different from previous controlled remote state preparation schemes which also utilize partially entangled channels, neither auxiliary qubits nor two-qubit unitary operations are required in our schemes, and our success probabilities are independent of the coefficients of quantum channels. The success probabilities are 50% and 25% for arbitrary single-qubit states and two-qubit states, respectively. We also show that the success probabilities can reach 100% for restricted classes of states.Moreover, we present a scheme for N-photon Greenberger-Horne-Zeilinger(GHZ) state analysis using hyperentanglement in polarization and time-bin degrees of freedom. We use time-bin degree of freedom as the ancillary and single-photon Bell state measurement to distinguish polarization Bell states and three-photon GHZ states, then we generalize it to the situation of N-photon GHZ states. Our scheme can be implemented non-locally with linear optics and a set of mutual orthogonal GHZ state can be distinguished deterministically with 100% success probabilities in theory.