| Quantum information is a new field of science and technology, which is developed as the combination of quantum mechanics and computation, information theory. Designing more powerful computer and more efficiency communication protocol are the goals of quantum information. In general, quantum information includes quantum cryptography, quantum computation and quantum communication, etc. A secure system based on the law of physics has been developed in quantum cryptography, and the practical secure system in fibers system will be soon achieved. In quantum computation, Some developments of the research of more powerful computer for faster computation speed or solving more complicated problem have been obtained in several quantum systems, such as: photons, trapped iron, cavity-QED, nuclear magnetic resonance (NMR), quantum dots and superconductor, etc. While in quantum communication, how to use quantum channel to transmit information more efficiency is the main problem. Two typical proposals are quantum teleportation and quantum dense coding which had been realized in optics system.Quantum communication is also to be practicability now, and how to choose suitable physics system for the realization of stable, fast, and reliable quantum communication is the main problem. In addition, similar to the theory of classical communication, the fundmental theory of quantum communication is required to be established. The dissertation includes some research in the linear optical realization of two schemes of quantum communication, and a pilot study in the theory of the capacity of the channel, which is the fundmental theory of quantum communication.1. Experimental proposal of probabilistic superdense coding with linear optical elementsQuantum superdense coding is an interesting scheme in quantum communication. Assisted by a pair of maximally entangled state, two bits of classical information can be extracted from just a single qubit sent by the sender. While the prior-shared entangled state is non-maximally, superdense coding can be completed only with some probability of success. In chapter III, firstly we realize the unambiguous discrimina- tion of the two non-orthogonal state with linear optical elements, then assisted with photon entanglement produced from parametric down-conversion, and postselection from the coincidence measurements, we propose a scheme of probabilistic superdense coding. The proposal is feasible with current experimental technology.2. Linear optical realization of qubit purification with the quantum amplitude damping channelIn the realistic computation or transmission processes, the qubits are inevitably coupled to the noisy environment, then the fidelity of the qubits would become lower. Qubit purification is a technique that through some quantum operations, one can extract a certain number qubits with higher fidelity from a set of mixed qubit states with the cost of a number of qubits. In chapter IV, we propose a scheme of linear optical realization of qubit purification with the quantum amplitude damping channel. In our proposal, it is including the simulation of the quantum amplitude damping channel, the realization of the optimal two-qubit purification and the discussions of arbitrary input qubits and arbitrary N qubits. Our scheme may be useful in transmission of photons in the fibers and it is feasible in the lab with the current experimental technology.3. Superadditivity in the quantum communicationIn quantum communication, by collective measurement the amount of information of n + m uses of the channel is larger than the summation of the amount of information of n uses and m uses of the channel. It is called superaddivity, which is a special property in quantum communication. In chapter V, we present the optimal measurement for a mixed-state ensemble transmitted after the quantum amplitude damping channel and calculate the amount of one-shot capacity. Then we prove the property of superadditivity is preserved when the mixed-state ensemble is used to transmit information.
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