Correlation Research On Quantum Entanglement Distribution In Multibody Systems

Quantum computation and quantum information are a brand-new promising interdisciplinary science subject integrating quantum mechanics and computer sci-ence.Quantum entanglement is not only one of the major characteristics that distinguish quantum from classical mechanics,but also an essential ingredient of quantum information theory.Quantum entanglement is one of the most important physical resources in quantum information processing.A lot of quantum informa-tion processing such as quantum teleportation,quantum dense coding,quantum key distribution and so on,can be achieved conditioned on quantum entanglement.The monogamy relation of entanglement is a way to characterise different types of entanglement distribution.The monogamy property can be interpreted as the fol-lowing statement:the amount of entanglement between A and B plus the amount of entanglement between A and C cannot be greater than the amount of entanglement between A and the BC pair.The first monogamy relation was named the Coffman-Kundu-Wootters(CKW)inequality.Osborne and Verstraete later proved that the CKW inequality also holds in an n-qubit system.The property of monogamy has been considered in many areas of physics:it can be used to extract an estimate of the quantity of information about a secret key captured by an eavesdropper in quantum cryptography.Monogamy plays an important role in the multi-level systems.Different types of entanglement correspond to different monogamy.This dissertation is mainly fo-cused on the generalised monogamy inequalities of convex-roof extended negativity(CREN)in multi-level systems.For monogamy inequalities,we analyze the rela-tionship between the concurrence and negativity,which is committed to explore a new description of the generalised monogamy inequalities.Furthermore,we show that the CREN of multi-qubit pure states satisfies some monogamy relations.We specifically test the generalised monogamy inequalities for qudits by considering the partially coherent superposition of a generalised W-class state in a vacuum,and we show that the generalised monogamy inequalities are satisfied in this case as well.The generalised monogamy is one of the most important physical resources in quantum information processing.The main work is as follows:1.We introduce several kinds of entanglement and discuss the relationship between them.Focus on the study of the monogamy inequalities correspondence of these entanglement.Finally,we introduce the generalised monogamy inequalities of convex-roof extended negativity.2.Based on the properties of linear entropy,we propose a generalised monogamy inequalities of convex-roof extended negativity of assistance,and extend it to multi-level systems.The relationship between convex-roof extended negativity of assis-tance is described by image.3.The generalised monogamy inequalities provide the upper and lower bounds of bipartite entanglement.It shows the bipartite entanglement between AB and the other qubits:especially under partition AB,a two-qubit system is different from the previous monogamy inequality that is typically used.4.First of all,we discuss the generalised monogamy inequalities by means of a high dimensional example with the dimension of the system being greater than or equal to two.Finally,we use the n-qudit pure state to show that the generalised monogamy inequalities is a good physical resource.