Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0611292 · The European Physical Journal D

Full separability criterion for tripartite quantum systems

Chi‐Shan Yu, H. S. Song

Published Dec 12, 2006• 4 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2006-00267-y

Related papers

Separability criterion of tripartite qubit systems

Chang‐shui Yu, He‐Shan Song

In this paper, we present a method to construct full separability criterion for tripartite systems of qubits. The spirit of our approach is that a tripartite pure state can be regarded as a three-order tensor that provides an intuitionistic mathematical formulation for the full separability of pure states. We extend the definition to mixed states and give out the corresponding full separability criterion. As applications, we discuss the separability of several bound entangled states, which shows that our criterion is feasible.

arXiv:quant-ph/0412104•Physical Review A•Aug 25, 2005•40 citations

Separability from Multipartite Measures

Chen-Te Ma, Ma-Ke Yuan

We show that multi-invariants provide necessary and sufficient criteria for full separability in finite-dimensional multipartite systems. For tripartite three-qubit states, the third-order negativity gives an exact criterion for full separability for both pure and mixed states. We then extend the framework to four-qubit pure states, whose full characterization requires eighteen independent real parameters. We identify eighteen independent entanglement measures, consisting of six bipartite, eight tripartite, and four quadripartite measures, with the third-order negativity serving as a key separability criterion. Finally, we generalize the construction to multipartite qudit systems and discuss an application to conformal field theory.

quant-pharXiv:2605.02097•Physical review. D/Physical review. D.•May 5, 2026•0 citations

Criteria for Separability of Multipartite Quantum System

Yuan-Hong Tao, Weiwei Ding, Chang’e Li

International Journal of Theoretical Physics•Nov 7, 2012•2 citations

SEPARABILITY OF MULTIPARTITE QUANTUM SYSTEMS

Ming Li, Wang Jing

Reports on Mathematical Physics•Feb 1, 2012•0 citations

LPP elementary operator criterion of full separability for states in multipartite quantum systems

Siqing Yan, Jinchuan Hou

Let H 1 , H 2 , …, H n , K ( n ⩾ 2) be complex Hilbert spaces of finite or infinite dimension. A necessary and sufficient criterion of full separability for multipartite states is established, which says that a state ρ in H 1 ⊗ H 2 ⊗⋅⋅⋅⊗ H n ⊗ K is fully separable if and only if (Λ⊗Id)ρ ⩾ 0 for all (finite-rank) LPP elementary operators Λ from into . Furthermore, a characterization of LPP elementary operators and a method of constructing LPP elementary operators by positive elementary operators are given. An example is also presented to demonstrate how to apply the criterion to detect entanglement of tripartite states.

Journal of Physics A Mathematical and Theoretical•Oct 10, 2012•5 citations

Separability criterion for quantum effects

Ikko Hamamura

arXiv:1709.07987•Physics Letters A•Jun 28, 2018•5 citations
In this paper, we present a method to construct full separability criterion for tripartite systems of qubits. The spirit of our approach is that a tripartite pure state can be regarded as a three-order tensor that provides an intuitionistic mathematical formulation for the full separability of pure states. We extend the definition to mixed states and give out the corresponding full separability criterion. As applications, we discuss the separability of several bound entangled states, which shows that our criterion is feasible.
We show that multi-invariants provide necessary and sufficient criteria for full separability in finite-dimensional multipartite systems. For tripartite three-qubit states, the third-order negativity gives an exact criterion for full separability for both pure and mixed states. We then extend the framework to four-qubit pure states, whose full characterization requires eighteen independent real parameters. We identify eighteen independent entanglement measures, consisting of six bipartite, eight tripartite, and four quadripartite measures, with the third-order negativity serving as a key separability criterion. Finally, we generalize the construction to multipartite qudit systems and discuss an application to conformal field theory.
Let H 1 , H 2 , …, H n , K ( n ⩾ 2) be complex Hilbert spaces of finite or infinite dimension. A necessary and sufficient criterion of full separability for multipartite states is established, which says that a state ρ in H 1 ⊗ H 2 ⊗⋅⋅⋅⊗ H n ⊗ K is fully separable if and only if (Λ⊗Id)ρ ⩾ 0 for all (finite-rank) LPP elementary operators Λ from into . Furthermore, a characterization of LPP elementary operators and a method of constructing LPP elementary operators by positive elementary operators are given. An example is also presented to demonstrate how to apply the criterion to detect entanglement of tripartite states.