scholarly journals Efficient nonlinear witnessing of non–absolutely separable states with lossy detectors

2021 ◽  
Vol 104 (3) ◽  
Author(s):  
Ayan Patra ◽  
Shiladitya Mal ◽  
Aditi Sen(De)
Keyword(s):  
Separable States

scholarly journals Non-separable states in a bipartite elastic system

AIP Advances ◽  
2017 ◽  
Vol 7 (4) ◽  
pp. 045020 ◽  
Author(s):  
P. A. Deymier ◽  
K. Runge
Keyword(s):  
Elastic System ◽  
Separable States

Entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states

2014 ◽  
Vol 14 (11&12) ◽  
pp. 937-948
Author(s):  
Eylee Jung ◽  
DaeKil Park
Keyword(s):  
Separable States ◽  
Qubit System ◽  
Symmetric States

In this paper we analyze entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states $\rho^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $\rho^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the relaxed Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of $\rho^{ES}$ are not dependent on $y_j \hspace{.2cm} (j=1,2,3)$ individually, but dependent on $y_1 + y_2 + y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.

scholarly journals CLASSICAL TENSORS AND QUANTUM ENTANGLEMENT I: PURE STATES

2010 ◽  
Vol 07 (03) ◽  
pp. 485-503 ◽  
Author(s):  
P. ANIELLO ◽  
J. CLEMENTE-GALLARDO ◽  
G. MARMO ◽  
G. F. VOLKERT
Keyword(s):  
Hilbert Space ◽  
Symplectic Geometry ◽  
Vector Fields ◽  
Riemannian Metric ◽  
Inner Product ◽  
Tensor Fields ◽  
Metric Tensor ◽  
Separable States ◽  
Pure States ◽  
Complex Projective

The geometrical description of a Hilbert space associated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here, we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.

scholarly journals Finding decompositions of a class of separable states

2012 ◽  
Vol 437 (10) ◽  
pp. 2613-2629 ◽  
Author(s):  
Erik Alfsen ◽  
Fred Shultz
Keyword(s):  
Separable States
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