The Effect Of Decoherence In Quantum Information

Quantum information is something that is encoded in the state of a quan-tum system. Recently, quantum information attracts much attentions. Quantum information have advantages over classical information. For example, quantum teleportation can transmit an unknown quantum state from a sender, called Al-ice, to a remote receiver, called Bob; dense coding can send two bits of classical information by transmitting one qubit; Shor's factoring algorithm presents a polynomial-time algorithm for factorization; Grover's search algorithm presents a quantum searching algorithm that reduces the computational complexity of current exhaustive search attacks from O(2N) to O(2N/2). Furthermore, the hard-ware of classical information becomes smaller and smaller and the behavior of the hardware is described by quantum mechanics.Although quantum information has so many advantages over classical infor-mation, the realization of quantum protocols is hard. Decoherence is one main obstacle in realizing quantum protocols. Decoherence is caused by the interaction between the system and its environment. When we design a quantum protocol, we assume that the quantum system does not suffer any unwanted interaction with its environment. Although fascinating conclusions can be drawn about the information processing tasks, these observations are tempered by the fact that in the real world there are no perfectly closed systems. Usually, decoherence loses quantum protocols the advantages. So, decoherence is an important topic in quantum information.We here investigate the effect of decoherence in quantum information. We in-vestigate the effect of decoherence in quantum resources (quantum entanglement, quantum discord, and quantum nonlocality), quantum computation (holonomic quantum computation and one-way quantum computation), quantum communi-cation (quantum teleportation). The main results are as follows:1)Because of quantum resources, quantum information has advantages over classical information. There are three kinds of resources in quantum information. They are quantum entanglement, quantum discord, and quantum nonlocality. Because of decoherence, quantum resources decrease, then the fidelities of the protocols of quantum information decrease. So, the effect of decoherence in quan-tum resources is a basic topic. We here investigate the effect of decoherence in quantum entanglement, quantum discord, and quantum nonlocality respectively. We distinguish the dynamics of entanglement between two choices for the initial conditions ρi(0) and ρ2(0), where pi(0) is prepared by the stochastic preparation procedure and ρ2(0) is prepared by the projective preparation procedure, and find that, for both the independent environment case and the common environment case, the projective preparation procedure is more detrimental to entanglement evolution than the stochastic preparation procedure. We investigate an entan-gled pair of spins in the noisy environment described by Ornstein-Uhlenbeck processes, and find that the quantum discord of some states is completely unaf-fected by independent Ornstein-Uhlenbeck noises for long intervals of time, and that the inevitable onset of the sudden decrease of the quantum discord can be substantially delayed by the decrease of the noise bandwidth r, where r-1=τc defines the environment's finite correlation time of the noise. We investigate the dynamics of measurement-induced nonlocality by exactly solving a model which consists of two independent atoms each subject to a zero-temperature muti-mode cavity. We find that the dynamics of measurement-induced nonlocality is discon-tinuity in some special conditions.2)Holonomic quantum computation is based on geometric phase. In order to combine the robust advantages of decoherence-free subspace (DFS) and the geometric phase, adiabatic holonomic quantum computation in DFS is proposed. It is known that adiabatic evolution is hard to control. In order to solve this problem, we show how to realize non-adiabatic holonomic quantum computation in DFSs. We use three neighboring physical qubits to encode one logical qubit and the three neighboring physical qubits are required to undergo the collective dephasing. Although the DFS of two neighboring physical qubits is the minimal DFS, we show that three neighboring physical qubits are necessary if one uses the dark states to realize non-adiabatic holonomic quantum computation in DFSs.3)Although quantum computation depends on quantum resource, the exact relation between them is unknown. One-way quantum computation is suitable to investigate this relation. We take a basic model, the rotational gate about the x axis based on the cluster state, and investigate the effects of noisy quantum chan-nels on the entanglement of cluster states and one way quantum computational gates. We try to investigate the behavior of the fidelity of the rotational gate when the entanglement sudden death (ESD) phenomenon happens. We find that the fidelity has no obvious discontinuity or special behavior at the points where ESD appears, although one-way quantum computation depends on quantum en-tanglement. Furthermore, the fidelity for bit-phase flip channel at α=π/2,3π/2is always equal to1while it is impossible for the other channels.4)Noisy quantum teleportation is one important topic. There are two kinds of researches in noisy quantum teleportation. The purpose of the first kind of research is to try to find out the fidelity of one channel state in different envi-ronments. The purpose of the second kind of research is to try to find out the fidelity of different channel states which have the same teleportation capacity in one environment. Our research belongs to the second kind of research. By con-sidering the local collective environments, we find the relation of the robustness between the GHZ state and the W state in terms of their teleportation capac-ity. We compare the GHZ state and the W state in terms of their robustness as resource states for teleportation in Pauli channels with memory and find the memory effect on this relation.