广义Concurrence及其应用-基础数学专业论文.docxVIP

This makes the second expression vector further clarified. In addition, the other condition is given. That is a linear combination of an inseparable vector with any vector. Two vectors |E1? ∈ HA ? HB ,|E2? ∈ HA ? HB , if |E2? is inseparable, then there are not more than two complex number λ such that |E1? + λ|E2? is separable. And, then there are not more than one complex number λ such that |E1? + λ|E2? is separable when |E1? ∈ HA ? HB is separable. In short, this chapter discusses all cases of combinations of the two two-body quantum linear states. In Chapter 4, the problem when the two-body mixed quantum state of rank 2 is separable is solved. There are two cases when the two-body mixed quantum state of rank 2 is separable. Now ρ = p|E1??E1| + (1 ? p)|E2??E2|, 0 p 1, ?E1|E2? = 0 is separable. Then one case is that |E1? and |E2? are separable. The other case is that |E1? and |E2? are inseparable, and there are two pure real or pure imaginary numbers making |E1? + λ|E2? separable. So, necessary and sufficient condition when the two-body mixed quantum state of rank 2 is separable is given. On this basis, we further study the two-body mixed quantum states of rank n(n ≥ 3). Some specific examples show that the conditions are not necessary are also given. It is convenient using Generalized Concurrence to determine whether the two-body quan- tum pure states are separable. So we solve all the problem whether the two-body mixed quantum state of rank 2 is separable. But, in the paper I can not solve all the problem when the rank is n(n ≥ 3). Whether the use of Generalized Concurrence is able to fully determine that two-body quantum states of rank n(n ≥ 3) is separable? Can the situation whether the linear combination of three pure quantum states is separable be all discussed? These problems are being further investigated. Key Words: Generalized Concurrence Maximum entanglement Separable pure states Separable mixed state VI 学位论文原创性声明 本人所提交的学位论文《广义的 Concurrence 及其应用》，是