Entanglement has a fundamental importance in quantum information processing, especially in quantum communication such as quantum teleportation. A reliable transfer of quantum information requires in general two parties, the sender and the receiver, to share pure entangled states. When a pure entangled state is distributed through a noisy quantum channel, however, the state becomes a mixed one, leading to an inaccurate transfer of information.
To solve this problem, various entanglement purification protocols(EPPs) are proposed. EPPs overcome the errors that occur during the transmission of a quantum state. Therefore, EPPs are related to quantum error correcting codes. Indeed, the concept of error detection can be usefully employed to construct and analyze the EPPs.
In this work, we systematically analyze, in the viewpoint of the error detection, the EPPs which extract a Bell state, or a generalized Bell state. We also discuss a general method to construct EPPs which obtain a pure GHZ-state. Furthermore, we propose two new EPPs, one extracting a generalized GHZ-state and the other extracting a W-state.
We then search a physical system where EPPs can be embodied experimentally. We choose a coherent state basis as a candidate for qubit(qudit) based information processing and discuss the characteristic of the coherent state qubit(qudit) system. Then we propose two teleportation schemes based on the coherent state qubit(qudit) system, one teleporting a qubit system and the other teleporting a qudit system. Finally, we propose a new EPP which extracts a quasi generalized Bell state against channel loss errors.
