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/0502062 · Physical Review A

Separability conditions from the Landau-Pollak uncertainty relation

Julio I. de Vicente, Jorge Sánchez-Ruiz

Published May 24, 2005• 29 citations
arXivHTMLPDF

Abstract

We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested and compared with previously stated criteria by applying them to states whose separability limits are already known. Our results are also extended to multipartite and higher-dimensional systems.

DOI
10.1103/physreva.71.052325

Related papers

Separability criterion in prime dimensions based on Landau-Pollak uncertainty relation

M. Yoshida, Takayuki Miyadera, Hideki Imai

We introduce a novel separability criterion for bipartite systems that consist of prime dimensional Hilbert spaces. We derive a strict Landau-Pollak uncertainty relation for observables related with MUB, which allows us to obtain the separability criterion. For the isotropic states, our criterion distinguishes the entangled states correctly.

International Symposium on Information Theory and its Applications•Dec 1, 2008•2 citations

Separability conditions from entropic uncertainty relations

Vittorio Giovannetti

We derive a collection of separability conditions for bipartite systems of dimension $d\ifmmode\times\else\texttimes\fi{}d$ which is based on the entropic version of the uncertainty relations. A detailed analysis of the two-qubit case is given by comparing the new separability conditions with existing criteria.

arXiv:quant-ph/0307171•Physical Review A•Jul 8, 2004•106 citations

Entanglement criteria via concave-function uncertainty relations

Yichen Huang

A general theorem as a necessary condition for the separability of quantum states in both finite and infinite dimensional systems, based on concave-function uncertainty relations, is derived. Two special cases of the general theorem are stronger than two known entanglement criteria based on the Shannon entropic uncertainty relation and the Landau-Pollak uncertainty relation, respectively; other special cases are able to detect entanglement where some famous entanglement criteria fail.

Physical Review A•Jul 29, 2010•107 citations

Characterizing Entanglement via Uncertainty Relations

Otfried Gühne

We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.

arXiv:quant-ph/0306194•Physical Review Letters•Mar 18, 2004•295 citations

Separability Criteria For Arbitrary Quantum Systems

Chang-shui Yu, He‐Shan Song

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.

arXiv:quant-ph/0412137•Dec 17, 2004•0 citations

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
We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested and compared with previously stated criteria by applying them to states whose separability limits are already known. Our results are also extended to multipartite and higher-dimensional systems.
We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.
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)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.