Advanced Realignment Criterion For Separability Of Quantum States

In the 20 th century,Quantum mechanics is another revolutionary theory in addition to relativity.Based on quantum mechanics,many strange phenomena have been found,especially quantum entanglement which is one of the most strange non-classical properties and was recognized by Einstein,Podolsky and Rosen in 1935.After that,many pivotal achievements such as Bell's inequality,Bohm theory,Aspect experiments were born,but the accurate definition of the entangled states was not given by Werner until 1989.In recent years,with the rapid progress in quantum information theory,it has become more and more clear that the entanglement is a basic quantum resource and acts as an important role in biology,other physical phenomena and the simulation of many body systems.At the same time,quantum communication and quantum computing,the two aspects of quantum information,continuously make breakthroughs.Therefore,the detection and quantification of entanglement are underlying problems.However,although in the past 20 years,a considerable amount of efforts are given,entanglement is not yet fully understand.In this dissertation,we mainly discuss the detection and quantification of entanglement in discrete variable systems.The main contents and results are follows: 1.The thesis summarizes main criteria in detail.For every criterion,we give a brief proof and illustrate the relationships with other criteria.2.First,the advanced realignment criterion is presented relies on advancedly realigned density matrix and trace norm.Second,we study the relationship between the new criterion and the other criteria,then come to the conclusion that the PPT criterion,the realignment criterion and the the optimized entanglement witness based on local orthogonal observables(LOOs)are all its special cases.Third,the results of two body and many body examples are given to illustrate our criterion is strong enough to identify bound entangled(BE)states,genuinely multipartite entanglement,entangled states with separable reduced density matrices and the maximally entangled states.At last,we apply our criterion to entanglement measures and derive a new negativity which is not only better than the original negativity,but also satisfies the basic properties of vanishing for separable states,convexity and invariant under local unitary transformations.