Classification On Multipartite Entanglement Structure With Quantum Fisher Information

The quantum entanglement is a fundamental different property from classical physics,and one of most important resource for next generation of quantum technology revolution.With the developing of quantum science,deeply understanding quantum state,especially the quantum structure of the multipartite quantum entanglement,is one of fundamental theoretical problem and also one of necessary practical problems.It is one of most challenging questions for understanding multipartite quantum states.We may understand it from the following two sides:(1)The efficient classification of multipartite entanglement could be the premier condition for further application of quantum states.Based on the density matrix description,there is relatively complete theory to quantify the quantum entanglement state.While with the increasing of the particles,it becomes very hard,or even impossible to measure the density matrix.That is the reason why we need to find an experimental friendly method.Basically,A multi-partite quantum entanglement can be split as many different partitions.This kind of partitions has been partially described by quantum depth and k-separability;(2)Another even hard basic problem is how to quantify the multipartite quantum entanglement.After carefully investigating the above questions,the theory of analysis based on the partitions of multi-partite quantum entanglement is developed in this thesis,with the help of quantum Fisher information.More specifically,we have found some interesting results by investigating the multipartite quantum states both for discrete variables and continuous variables.The main points are:For discrete variable multipartite quantum entanglement state,considering the corresponding relationship between the integer number partition theory and the structure of multipartite quantum entanglement state,we investigated the partitions based on their Young diagram.Based on two experimental measurable quantities,quantum Fisher information and spin squeezing coefficients,an analytical formula for describing the partitions of quantum state is presented.And the efficient criteria on multipartite quantum entanglement are proved.Our results shows: quantum depth and k-separability can be two limit cases,and Dyson rank can be one efficient parameter;the availabilities of our criteria are proved by analyzing the published experimental results on atom.For the continuous variable quantum states,we studied the entanglement structure of controllable losses,multimode(up to 4 modes)continuous-variable Gaussian quantum states by applying the criteria based on quantum Fisher information.Our results show that this criterion is helpful tools to explore the geometrical structure of multi-mode Gaussian entanglement states.Compared with PPT criteria,there are two advantages in the following two sides: usefulness for quantum states with more than two partitions and also for non-Gaussian states.We also found its limitation on bipartition quantum entanglement analysis.The losses did not make any effect on its usefulness.