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:0711.4282 · Physical Review Letters

Experimentally Friendly Geometrical Criteria for Entanglement

Piotr Badziąg, Časlav Brukner, Wiesław Laskowski, Tomasz Paterek, Marek Żukowski

Published Apr 8, 2008• 79 citations
arXivHTMLPDF

Abstract

A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.
DOI
10.1103/physrevlett.100.140403

Related papers

Experimentally accessible geometrical separability criteria

Piotr Badziąg, Časlav Brukner, Wiesław Laskowski +2 more

We present an intuitive geometrical approach to entanglement detection. It allows one to formulate simple and experimentally feasible sufficient conditions for entanglement. Within the approach we derive the necessary and sufficient condition for separability and discuss its relation with entanglement witnesses and positive maps.

Physica Scripta•Jul 1, 2009•1 citation

Unified approach to geometric and positive-map-based nonlinear entanglement identifiers

Marcin Markiewicz, Adrian Kołodziejski, Zbigniew Puchała +3 more

Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case, i.e., two-partite quantum systems. Here we provide an analysis of whether there exists a relation between two of the most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in the laboratory and the second one a geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct experimentally friendly entanglement criteria.

arXiv:1802.00806•Physical Review A•Apr 24, 2018•2 citations

Simple sufficient condition for subspace entanglement

Maciej Demianowicz, Grzegorz Rajchel-Mieldzioć, Remigiusz Augusiak

We introduce a simple sufficient criterion allowing to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its applicability in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the $d$--level Dicke states.

•Jul 15, 2021•0 citations

Simple Sufficient Criteria for Optimality of Entanglement Witnesses

Frederik vom Ende, Simon Cichy

If one wants to establish optimality of a given bipartite entanglement witness, the current standard approach is to check whether it has the spanning property. Although this is not necessary for optimality, it is most often satisfied in practice, and for small enough dimensions or sufficiently structured witnesses this criterion can be checked by hand. In this work we introduce a novel characterization of the spanning property via entanglement-breaking channels, which in turn leads to a new sufficient criterion for optimality. This criterion amounts to just checking the kernel of some bipartite state. It is slightly weaker than the spanning property, but it is a lot easier to test for -- by hand as well as numerically -- and it applies to almost all witnesses which are known to have the spanning property. A second criterion is derived from this, where one can simply compute the expectation value of the given witness on a maximally entangled state. Finally, this approach implies new spectral constraints on witnesses as well as on positive maps.

arXiv:2505.15615•May 21, 2025•0 citations

Simple sufficient condition for subspace to be completely or genuinely entangled

Maciej Demianowicz, Grzegorz Rajchel-Mieldzioć, Remigiusz Augusiak

Abstract We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the d -level Dicke states.

arXiv:2107.07530•New Journal of Physics•Sep 27, 2021•10 citations

A Necessary and Sufficient Condition for Entanglement Witness

Fabio Masillo

In this paper we introduce a criterion for the characterization of Entanglement Witness for multipartite quantum systems. Our approach is based on the characterization of the "tangent space" to the set of pure product states.

arXiv:1204.6052•Apr 26, 2012•0 citations
Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case, i.e., two-partite quantum systems. Here we provide an analysis of whether there exists a relation between two of the most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in the laboratory and the second one a geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct experimentally friendly entanglement criteria.
We introduce a simple sufficient criterion allowing to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its applicability in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the ddd--level Dicke states.
If one wants to establish optimality of a given bipartite entanglement witness, the current standard approach is to check whether it has the spanning property. Although this is not necessary for optimality, it is most often satisfied in practice, and for small enough dimensions or sufficiently structured witnesses this criterion can be checked by hand. In this work we introduce a novel characterization of the spanning property via entanglement-breaking channels, which in turn leads to a new sufficient criterion for optimality. This criterion amounts to just checking the kernel of some bipartite state. It is slightly weaker than the spanning property, but it is a lot easier to test for -- by hand as well as numerically -- and it applies to almost all witnesses which are known to have the spanning property. A second criterion is derived from this, where one can simply compute the expectation value of the given witness on a maximally entangled state. Finally, this approach implies new spectral constraints on witnesses as well as on positive maps.
Abstract We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the d -level Dicke states.