Research On The Robustness Of Entanglement And Generalized Robustness Of Entanglement

In quantum information and quantum computation theory, as an important resource of quantum information processing, the evolution rule of quantum entan-glement leads to more and more attentions. In order to reveal entangled ability of a quantum system, Vidal and Tarrach introduced the concept of entanglement robust-ness(RoE), which quantifies in a sense the endurance of entanglement against noise and jiamming; Michael Steiner generalized this concept and then defined the gen-eralized robustness entanglement(GRoE). At first, we construct a class of TV-states and discuss their RoE and GRoE. Furthermore, we study the related properties of GRoE, we obtain the necessary and sufficient conditions for a quantum channel to decrease (resp. increase, maintain) the GRoE of all quantum states, and thus get some corollaries. This paper is divided into four chapters and arranged as follows:In Chapter 1, we introduce some research backgrounds and status on our main contents, some basic definitions and theorems.In Chapter 2, we discuss the RoE of the IV-states. Firstly, we find upper and lower bounds for RoE, and obtain some conditions for the upper bounds and the lower bounds to be equal. At last, under the obtained conditions, we compute the RoE of W-states.In Chapter 3, we discuss upper and lower bounds for GRoE and obtain some conditions for the upper bounds and the lower bounds to be equal. The GRoE of W-states is then computed under the obtained conditions. As a special case of W-states, it is proved that RoE and GRoE of W-states are equal and then the related optimal and generalized optimal states are also found. Lastly, it is proved that the GRoE function is lower semi-continuous on the set of all quantum states of multi-partite system.In Chapter 4, we study the influences of quantum channels on the generalized robustness of multi-partite entanglement. Firstly, based on the fact that the set of all separable states is closed and convex, it is proved that the infimum in the definition of GRoE in [15] can be attained and the reasonableness of the definition of the GRoE is then illustrated; secondly, it is proved that a convex combination of two different generalized optimal states of an entanglement state is still a generalized optimal state; lastly, necessary and sufficient conditions for a quantum channel to decrease (resp. increase, maintain) the GRoE of all quantum states are obtained.