Quantum Operations Implemented By Remote Parters

Quantum information and quantum computation is an interdisciplinary research field among classical computation, classical information and quantum mechanics. In recent years, it is developed rapidly. Theoretically, quantum computation is very powerful. Using quantum computation, some "difficult" problem in classical computation can be effectively solved, the most striking example being the factorization of large numbers. In actual application, the quantum computer should have an enough big size. However, effects such as decoherence and dissipation make the constuction of a computer of many qubits difficult. To solve this problem, distributed quantum computation is proposed, alike the classical distributed computation and classical network.The basic elements of distributed quantum computation are remote implementation of quantum operations and local implementation of nonlocal operations. It is a basic problem to find methods using only local operations, classical communications and shared entanglements (LOCCSR) to accomplish these tasks. Entanglement resources are important and precious in quantum information process, and classical communications relate to the speed of computation. So, it is important to accomplish these tasks using the least entanglement resources and classical communications. Researchs about this issue are also important for understanding quantum operations better. Main contents of this dissertation are how to accomplish this tasks using resources as few as possible.1. Remote implementation of local quantum operations.Remote implementation of local quantum operations may be understood as quantum operation being transferred from a local system to a remote system without physically sending the device only using LOCCSE. If the operation is unknown, it can only be remotely implemented via bidirectional quantum state teleportation (BQST). If the operation is partially known, it can be remotely implemented using less resources. Huelga etc. and Wang respectively researched the problem of remote implementation of quantum operation in some special restricted sets, and they also proposed the corresponding optimal protocols (HPV and Wang). Here, "optimal" means using the least entanglement resources and classical communications.We consider these results as a whole, and propose an optimal protocol for a class of quantum operations with block forms, and above protocols (BQST, HPV, Wang) can all be regarded as a special form of this protocol. Most of the important operations has a form of block matrices, such as the contolled-U operations. But, such operations cannot be remotely implemented using HPV or Wang protocol, and it requires more resources if using BQST. Our protocol give an optimal method to implement such operations.2. Local implementation of nonlocal quantum operations.Local implementation of nonlocal quantum operations is implementation of a nonlocal operation on qubits of two or more parters using LOCCSE. BQST method can be used for any operations, but if the operation has some forms, it may be implemented using less resources. Eisert etc. researched several important nonlocal operations, and they proposed a protocol for Cnot operation and controlled-U operations using only the half resources of BQST.We demonstrated that a similar protocal can be used for any operation with diagonal block or offdiagonal block forms, even if the detail of the operation is unknown. This protocol is independent with the dimension of the block. We also generalized these results to the two parter multiqubit cases and the multiparty cases.In multipary cases, GHZ states are also important. We propose a protocol to implement consecutive two diagnal block operations using one shared GHZ state. The protocol can be used to implement the Cnot operation of two targets. We demonstrate that one shared GHZ state is necessary for this operation.In this dissertation, we will introduce the fundament of quantum information and quantum computation in chapter one. Then, we will disscuss the remote implementation of local quantum operations in chapter two and disscuss the local implementation of nonlocal operations in chapter three. Finally, we will summarize the dissertation in chapter four.