Detection of genuine entanglement for multipartite quantum states

Improved tests of genuine entanglement for multiqudits

“…sharper than that of [29] in this case. Actually in general, our bound is almost always significantly stronger than that of [29]. For instance when…”

“…In another situation, let α = 1, β = 0.03, γ = 1, ρ is GME when 0.81 < x ≤ 1, which is better than the interval 0.82 ≤ x ≤ 1 given in [29] for α = 1, β = 1 given in [29] (here the latter β corresponds to our γ).…”

“…Substituting ( 18) into ( 17), we get Remark 2. Note that the first term of the bound is exactly that of [29]. For the case D ≥ d 2 , the second term…”

“…We can apply Theorem 1 to locate a range of x where ρ is GME. Specifically, let α = 0, β = 0, γ = 1, then Theorem 1 implies that when 0.51 < x ≤ 1, ρ is GME, which is larger than the range 0.53 ≤ x ≤ 1 given in [29] (here we have corrected the theorem therein). We have compiled a comparison of several choices of the parameters α, β, γ in table 1, which clearly shows that our criterion detects a greater GME region than that of [29].…”

“…separability tests were given by using the Bloch representation [28], by the matrix method [29], by the upper bound of the Bloch vectors [30], and by using witness operators [31]. Detection of genuine tripartite entanglement was given by multiple sequential observers [32], and by local marginals [33].…”