Bound Entanglement for Bipartite and Tripartite Quantum Systems

Zhao, Hui; Guo, Sha

doi:10.1007/s10773-015-2563-9

Cited by 1 publication

(5 citation statements)

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“…According to [19], the state ρ is PPT and violates the range criterion. From Theorem 1 ρ ′ is PPT too.…”

Section: Remark 3 Instead Of the Operator Q In The Theorem 1 If Onementioning

confidence: 99%

“…In [19], we have presented a class of bound entangled states in 3k ⊗ 3k quantum systems. Using Theorem 1, we can construct new bound entangled states from these 3k ⊗ 3k bound entangled states.…”

Section: Construction Via Operators Acting On Density Matrixmentioning

confidence: 99%

“…Example 3. The spectral decomposition of the bound entangled state ρ [19] in 3k ⊗ 3k quantum systems is written as follows:…”

Section: Construction Via Operators Acting On Density Matrixmentioning

confidence: 99%

“…High-dimensional bipartite and multipartite bound entangled states are studied in Ref. [15,16,17,19]. Although many bound entangled states have been found, the physical character and mathematical structure of bound entangled states are still not well understood.…”

Section: Introductionmentioning

confidence: 99%

“…where ij denotes the product of a finite number matrices P ij , similar results can be obtained.Next we will give some examples. The spectral decomposition of the state ρ[19] in 3 ⊗ 3 systems can be expressed as,…”

mentioning

confidence: 99%

See 4 more Smart Citations

Construction of bound entangled states based on permutation operators

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Guo

Jing

et al. 2015

Quantum Inf Process

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We present a construction of new bound entangled states from given bound entangled states for arbitrary dimensional bipartite systems. One way to construct bound entangled states is to show that these states are PPT (positive partial transpose) and violate the range criterion at the same time. By applying certain operators to given bound entangled states or to one of the subsystems of the given bound entangled states, we obtain a set of new states which are both PPT and violate the range criterion. We show that the derived bound entangled states are not local unitary equivalent to the original bound entangled states by detail examples.

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“…According to [19], the state ρ is PPT and violates the range criterion. From Theorem 1 ρ ′ is PPT too.…”

Section: Remark 3 Instead Of the Operator Q In The Theorem 1 If Onementioning

confidence: 99%

Section: Construction Via Operators Acting On Density Matrixmentioning

confidence: 99%

“…Example 3. The spectral decomposition of the bound entangled state ρ [19] in 3k ⊗ 3k quantum systems is written as follows:…”

Section: Construction Via Operators Acting On Density Matrixmentioning

confidence: 99%