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

Chinese Physics B

On a biseparability criterion of bipartite qudit state

Bilal Benzimoun, Mohammed Daoud A

Published Aug 1, 2019• 2 citations
Publisher

Abstract

In this paper, we propose a new approach to tackle the separability problem for bipartite qudit mixed-states. This is based on the Majorana representation which allows to represent a N-spinors (qudit) as a symmetric state of N spin-1/2. We also discuss how we can exploit such representation and the notion of the biseparability of multipartite qubit states in the sense to establish new criteria of the separability problem based on the PPT and concurrence.

DOI
10.1088/1674-1056/28/8/080302

Related papers

CRITERIA OF PARTIAL SEPARABILITY OF MULTIPARTITE QUBIT MIXED STATES

Zai-Zhe Zhong

We discuss the partial separability and its criteria problems of multipartite qubit mixed states. First, we strictly define what is the partial separability of a multipartite qubit system. Next, we provide a way of reduction from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that an N-partite qubit mixed state to be partially separable is its reduction to satisfy the PPT condition.

arXiv:quant-ph/0409182•International Journal of Quantum Information•May 31, 2005•2 citations

Separability Criterion for Bipartite States and Its Generalization to Multipartite Systems

Jie‐Hui Huang, Liyun Hu, Lei Wang +1 more

A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. All the symmetric operators, represented by a symmetric matrix with only two nonzero elements, and their arbitrary linear combinations are found to be entanglement witnesses. By using these symmetric operators, Wootters' separability criterion for two-qubit states can be generalized to bipartite and multipartite systems in arbitrary dimensions.

arXiv:1212.0082•Chinese Physics Letters•Apr 1, 2014•2 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

Quantum separability criteria for arbitrary-dimensional multipartite states

Ming Li, Jing Wang, Shao-Ming Fei +1 more

We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our criteria are more powerful than the positive partial transposition criterion, the realignment criterion, and the criteria based on the correlation matrices.

arXiv:1402.4428•Physical Review A•Feb 18, 2014•59 citations

Separability criteria based on Heisenberg–Weyl representation of density matrices

Jingmei Chang, Meiyu Cui, Tinggui Zhang +1 more

Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg–Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.

arXiv:2002.00164•Chinese Physics B•Mar 1, 2018•9 citations

Separability from spectrum for qubit-qudit states

Nathaniel Johnston

The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states $\ensuremath{\rho}$ with the property that ${U}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\rho}U$ is separable for all unitary matrices $U$. This problem has been solved when the local dimensions $m$ and $n$ satisfy $m=2$ and $n\ensuremath{\le}3$. We solve all remaining qubit-qudit cases (i.e., when $m=2$ and $n\ensuremath{\ge}4$ is arbitrary). In all of these cases we show that a state is separable from spectrum if and only if ${U}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\rho}U$ has positive partial transpose for all unitary matrices $U$. This equivalence is in stark contrast with the usual separability problem, where a state having positive partial transpose is a strictly weaker property than it being separable.

arXiv:1309.2006•Physical Review A•Dec 23, 2013•65 citations
In this paper, we propose a new approach to tackle the separability problem for bipartite qudit mixed-states. This is based on the Majorana representation which allows to represent a N-spinors (qudit) as a symmetric state of N spin-1/2. We also discuss how we can exploit such representation and the notion of the biseparability of multipartite qubit states in the sense to establish new criteria of the separability problem based on the PPT and concurrence.
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.
The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states $\ensuremath{\rho}$ with the property that ${U}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\rho}U$ is separable for all unitary matrices UUU. This problem has been solved when the local dimensions mmm and nnn satisfy m=2m=2m=2 and $n\ensuremath{\le}3$. We solve all remaining qubit-qudit cases (i.e., when m=2m=2m=2 and $n\ensuremath{\ge}4$ is arbitrary). In all of these cases we show that a state is separable from spectrum if and only if ${U}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\rho}U$ has positive partial transpose for all unitary matrices UUU. This equivalence is in stark contrast with the usual separability problem, where a state having positive partial transpose is a strictly weaker property than it being separable.