Speed Of Disentanglement And Robustness Of Entanglement In The Mutiqubit Systems

Quantum entanglement is one of the non-classical properties and used for actingas an important resource of quantum information. In recently, quantum decoherenceand quantum entanglement dynamics attract much internationally from physicists. Inthis thesis, the introduction about quantum theory is given firstly. Then, the quantumentanglement and quantum decoherence are introduced briefly. Lastly, we investigatethe speed of disentanglement and the entanglement robustness in the multi-qubitsystems under the local depolarizing channel, in which each qubit is independentlycoupled to the environment. We focus on the bipartition entanglement between onequbit and the remaining qubits constituting the system, which is measured by thenegativity. For the two-qubit system, the speed of the pure state depends on itsentanglement completely. The upper and lower bounds of the speed for arbitrarytwo-qubit states, and the necessary conditions for a state achieving them, are obtained.For the three-qubit system, we study the speed for pure states, whose entanglementproperties can be completely described by five local unitary transformation invariants.An analytical expression of the relation between the speed and the invariants isderived. In the k-qubit systems, we mainly study three kinds of states, such asGreenberger-Horne-Zeilinger (GHZ) state, W state, and the superposition of them, foran arbitrary superposition of GHZ state and W state, the speed depends almostentirely on the amount of the negativity when k increases to five or six. An alternativequantitative definition for the robustness of entanglement is presented based on thespeed of disentanglement, with comparison to the widely studied robustness measuredby the critical amount of noise parameter where the entanglement vanishes. In thelimit of large number of particles, the alternative robustness of the GHZ-type states isinversely proportional to k, and the one of the W states approaches.