2015
DOI: 10.1142/s0219749915500367
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Bound entanglement and distillability of multipartite quantum systems

Abstract: We construct a class of entangled states in $\mathcal{H}=\mathcal{H}_{A}\otimes\mathcal{H}_{B}\otimes\mathcal{H}_{C}$ quantum systems with $dim\mathcal{H}_{A}=dim\mathcal{H}_{B}=dim\mathcal{H}_{C}=2$ and classify those states with respect to their distillability properties. The states are bound entanglement for the bipartite split$(AB)-C$. The states are NPT entanglement and $1$-copy undistillable for the bipartite splits $A-(BC)$ and $B-(AC)$. Moreover, we generalize the results of $2\otimes2\otimes2$ systems… Show more

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Cited by 2 publications
(5 citation statements)
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“…Actually, this special case is very common in many interesting models [26,33,27,15] in which the exact O or Q operators just contain no noises. Moreover, in general case, we can still expand O and Q into functional series and only taking the first term (with zeroth order of noise variables) of the expansions as…”
Section: General Stochastic Schrödinger Equationmentioning
confidence: 99%
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“…Actually, this special case is very common in many interesting models [26,33,27,15] in which the exact O or Q operators just contain no noises. Moreover, in general case, we can still expand O and Q into functional series and only taking the first term (with zeroth order of noise variables) of the expansions as…”
Section: General Stochastic Schrödinger Equationmentioning
confidence: 99%
“…Fundamentally, the dynamics of open quantum systems embedded in one or more environments has attracted the wide-spread interest in recent years [5,6,7,8]. On the one hand, the temporal behaviours of quantum open systems are essential for understanding many fundamental issues of quantum theory such as quantum dissipation and decoherence [9,10,11,12,13,14,15]. On the other hand, many novel applications based on quantum devices also require a better understanding on the interaction between the quantum system of interest and its environment in order to manipulate and control the system's dynamics [16,17].…”
Section: Introductionmentioning
confidence: 99%
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“…In fact, since ρ is PPT, ρ ′ is also PPT. By [18], the following vectors form a basis of the range of ρ: |ψ 3m−2,3m−2 = (0, · · · , 0, a 3m−2 , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3m−2 , 0, · · · , 0) t , |ψ 3m−2,3n−2 = (0, · · · , 0, a 3m−2 , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3n−2 , 0, · · · , 0) t , |ψ 3m−2,3n−1 = (0, · · · , 0, a 3m−2 , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3n−1 , 0, · · · , 0) t , |ψ 3m−2,3n = (0, · · · , 0, a 3m−2 , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3n , 0, · · · , 0) t , |ψ 3m−1,3m−1 = (0, · · · , 0, a 3m−1 , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3m−1 , 0, · · · , 0) t , |ψ 3m−1,3n−2 = (0, · · · , 0, a 3m−1 , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3n−2 , 0, · · · , 0) t , |ψ 3m−1,3n−1 = (0, · · · , 0, a 3m−1 , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3n−1 , 0, · · · , 0) t , |ψ 3m,3m = (0, · · · , 0, a 3m , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3m , 0, · · · , 0) t , |ψ 3m,3n−2 = (0, · · · , 0, a 3m , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3n−2 , 0, · · · , 0) t , |ψ 3m,3n = (0, · · · , 0, a 3m , 0, · · · , 0) t ⊗ (0, · · · , 0, b 3n , 0, · · · , 0) t ,…”
Section: Remark 3 Instead Of the Operator Q In The Theorem 1 If Oneunclassified
“…In fact, since ρ is PPT, ρ ′ is also PPT. By [18], the following vectors form a basis of the range of ρ:…”
Section: Construction Via Operators Acting On Density Matrixmentioning
confidence: 99%