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/0412137

Separability Criteria For Arbitrary Quantum Systems

Chang-shui Yu, He‐Shan Song

Published Dec 17, 2004• 0 citations
arXivHTMLPDF

Abstract

The purpose of this paper is to obtain a sufficient and necessary condition as a criteria to test whether an arbitrary multipartite state is entangled or not. Based on the tensor expression of a multipartite pure state, the paper shows that a state is separable iff $| \mathbf{C}(ρ)| $ =0 for pure states and iff $C(ρ)$ vanishes for mixed states.

DOI
10.48550/arxiv.quant-ph/0412137

Related papers

On sufficient and necessary criteria of multipartite quantum entanglement

Zhi-Bo Chen, Shao-Ming Fei

Abstract Based on the generalized Bloch representation, we study the separability and entanglement of arbitrary dimensional multipartite quantum states. Some sufficient and some necessary criteria are presented. For certain states, these criteria together are both sufficient and necessary. Detailed examples show that our criteria are better than some existing ones in identifying separability. Based on these criteria, the largest separable ball around the maximally mixed state for arbitrary multi-qubit systems is found, and it is proved that its radius defined via the l 1-norm of the Bloch vector is the constant 1. Furthermore, the criteria in this paper can be implemented experimentally.

arXiv:2503.10123•Physica Scripta•Aug 8, 2025•0 citations

Efficient entanglement criteria for discrete, continuous, and hybrid variables

Manuel Gessner, Luca Pezzè, Augusto Smerzi

We develop a method to construct entanglement criteria for arbitrary multipartite systems of discrete or continuous variables and hybrid combinations of both. While any set of local operators generates a sufficient condition for entanglement of arbitrary quantum states, a suitable set leads to a necessary and sufficient criterion for pure states. The criteria are readily implementable with existing technology and reveal entanglement that remains undetected by the respective state-of-the-art methods for discrete and continuous variables.

arXiv:1608.02421•Physical Review A•Aug 1, 2016•75 citations

Separability criteria for multipartite quantum mixed states

Zhou Hui

The separability of mixed states in multipartite quantum systems is investigated. If a quantum state in a multipartite system with an arbitrary dimension is separable, some quantity in relation to Hermitian matrix is positive.

Chinese Physics•Jan 27, 2005•3 citations

k-separability criterion of mixed multipartite quantum states

Ting Gao, Yan Hong

The $k$-separability of mixed $n$-partite ($n\geq 3$) quantum states is mainly discussed in this paper. We obtain practical $k$-separability criteria to identify $k$-nonseparable mixed multipartite states in arbitrary dimensional quantum systems and detect genuine $n$-partite entanglement ($k=2$) and entanglement ($k=3$) which have previously not been identified. No optimization or eigenvalue evaluation is needed, our criteria can be evaluated by simple computations involving components of the density matrix and can be implemented in today's experiments.

•Apr 13, 2012•2 citations

Separability Criteria for Quantum Mixed States

Hui Zhao, Zhi‐Xi Wang

We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in quantum systems) is separable, we show that some quantity in relation to Hermitian matrix is positive.

Communications in Theoretical Physics•Oct 15, 2004•6 citations

Separability criterion for pure states in multipartite and high dimensional systems

An Min Wang

We propose a sufficient and necessary separability criterion for pure states in multipartite and high dimensional systems. Its main advantage is operational and computable. The obvious expressions of this criterion can be given out by the coefficients of components of the pure state. In the end, we simply mention a principle method how to define and obtain the measures of entanglement in multipartite and high dimensional systems.

arXiv:quant-ph/0207136•Jul 23, 2002•0 citations
The purpose of this paper is to obtain a sufficient and necessary condition as a criteria to test whether an arbitrary multipartite state is entangled or not. Based on the tensor expression of a multipartite pure state, the paper shows that a state is separable iff ∣C(ρ)∣| \mathbf{C}(ρ)| ∣C(ρ)∣ =0 for pure states and iff C(ρ)C(ρ)C(ρ) vanishes for mixed states.
Abstract Based on the generalized Bloch representation, we study the separability and entanglement of arbitrary dimensional multipartite quantum states. Some sufficient and some necessary criteria are presented. For certain states, these criteria together are both sufficient and necessary. Detailed examples show that our criteria are better than some existing ones in identifying separability. Based on these criteria, the largest separable ball around the maximally mixed state for arbitrary multi-qubit systems is found, and it is proved that its radius defined via the l 1-norm of the Bloch vector is the constant 1. Furthermore, the criteria in this paper can be implemented experimentally.
We develop a method to construct entanglement criteria for arbitrary multipartite systems of discrete or continuous variables and hybrid combinations of both. While any set of local operators generates a sufficient condition for entanglement of arbitrary quantum states, a suitable set leads to a necessary and sufficient criterion for pure states. The criteria are readily implementable with existing technology and reveal entanglement that remains undetected by the respective state-of-the-art methods for discrete and continuous variables.
The kkk-separability of mixed nnn-partite (n≥3n\geq 3n≥3) quantum states is mainly discussed in this paper. We obtain practical kkk-separability criteria to identify kkk-nonseparable mixed multipartite states in arbitrary dimensional quantum systems and detect genuine nnn-partite entanglement (k=2k=2k=2) and entanglement (k=3k=3k=3) which have previously not been identified. No optimization or eigenvalue evaluation is needed, our criteria can be evaluated by simple computations involving components of the density matrix and can be implemented in today's experiments.