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Publisher’s Note: Inseparability Criteria for Continuous Bipartite Quantum States [Phys. Rev. Lett.95, 230502 (2005)]

Evgeny V Shchukin, W. Vogel

Physical Review LettersDec 8, 20056 citations

Comment on: Local Unitary Equivalence of Multipartite Pure Qubits States

Ana María Guerra Martins

A Comment on the Letter by B. Kraus {\it Phys. Rev. Lett.}{\bf 104}, 020504 (2010).

arXiv:1407.4634Jul 17, 20140 citations

Inseparability criteria based on matrices of moments

Adam Miranowicz, Marco Piani, Paweł Horodecki +1 more

Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. 95, 230502 (2005)]. If a state is separable, then the corresponding matrix of moments is separable too. Thus, we derive generalized criteria based on the separability properties of the matrix of moments. In particular, a criterion based on realignment of moments in the matrix is proposed as an analog of the standard realignment criterion for density matrices. Other inseparability inequalities are obtained by applying positive maps to the matrix of moments. Usefulness of the Shchukin-Vogel criterion to describe bipartite-entanglement of more than two modes is demonstrated: we obtain various three-mode inseparability criteria, including some previously known ones, which were originally derived from the Cauchy-Schwarz inequality.Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. 95, 230502 (2005)]. If a state is separable, then the corresponding matrix of moments is separable too. Thus, we derive generalized criteria based on the separability properties of the matrix of moments. In particular, a criterion based on realignment of moments in the matrix is proposed as an analog of the standard realignment criterion for density matrices. Other inseparability inequalities are obtained by applying positive maps to the matrix of moments. Usefulness of the Shchukin-Vogel criterion to describe bipartite-entanglement of more than two modes is demonstrated: we obtain various three-mode inseparability criteria, including some previously known ones, which were originally derived from the Cauchy-Schwarz inequality.

arXiv:quant-ph/0605001Physical Review ANov 3, 200979 citations

Comment on “Criteria for Separability of Multipartite Quantum System”

Da‐Wei Chang

International Journal of Theoretical PhysicsDec 15, 20140 citations

Optimizing confidence in negative-partial-transpose-based entanglement criteria

Lydia A. Kanari-Naish, Clarke, Jack, Sofia Qvarfort +1 more

A key requirement of any separable quantum state is that its density matrix has a positive partial transpose. For continuous bipartite quantum states, violation of this condition may be tested via the hierarchy of negative-partial-transpose (NPT) based entanglement criteria introduced by Shchukin and Vogel [Phys. Rev. Lett. 95, 230502 (2005)]. However, a procedure for selecting the optimal NPT-based criterion is currently lacking. Here, we develop a framework to select the optimal criterion by determining the level of confidence of criteria within the Shchukin and Vogel hierarchy for finite measurement number, environmental noise, and the optimal allocation of measurement resources. To demonstrate the utility of our approach, we apply our statistical framework to prominent example Gaussian and non-Gaussian states, including the two-mode squeezed vacuum state, the quanta-subtracted two-mode squeezed vacuum state, and the two-mode Schrödinger-cat state. Beyond bipartite inseparability tests, our framework can be applied to any Hermitian matrix constructed of observable moments and thus can be utilized for a wide variety of other nonclassicality criteria and multi-mode entanglement tests.A key requirement of any separable quantum state is that its density matrix has a positive partial transpose. For continuous bipartite quantum states, violation of this condition may be tested via the hierarchy of negative-partial-transpose (NPT) based entanglement criteria introduced by Shchukin and Vogel [Phys. Rev. Lett. 95, 230502 (2005)]. However, a procedure for selecting the optimal NPT-based criterion is currently lacking. Here, we develop a framework to select the optimal criterion by determining the level of confidence of criteria within the Shchukin and Vogel hierarchy for finite measurement number, environmental noise, and the optimal allocation of measurement resources. To demonstrate the utility of our approach, we apply our statistical framework to prominent example Gaussian and non-Gaussian states, including the two-mode squeezed vacuum state, the quanta-subtracted two-mode squeezed vacuum state, and the two-mode Schrödinger-cat state. Beyond bipartite inseparability tests, our framework can be applied to any Hermitian matrix constructed of observable moments and thus can be utilized for a wide variety of other nonclassicality criteria and multi-mode entanglement tests.

arXiv:2502.19624Feb 26, 20250 citations

A sufficient and necessary criterion for separability of bipartite quantum states

Zhao, Hui Hui, Yu +1 more

中国物理B：英文版Jan 1, 20140 citations

Comment on “Inseparability Criteria for Continuous Bipartite Quantum States”

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Comment on “Inseparability Criteria for Continuous Bipartite Quantum States”

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