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

Symmetry

The Separability Problem in Two Qubits Revisited

Honorine Gnonfin, Laure Gouba

Published Nov 20, 2023• 4 citations
Publisher

Abstract

In this paper, we present an overview of the progress in the separability problem in bipartite systems, more specifically in a two quantum bits (qubits) system, from the separability criterion based on Bell’s inequalities in 1964 to the recent separability criteria.
DOI
10.3390/sym15112089

Related papers

Quantum entanglement: an overview of the separability problem in two quantum bits

Honorine Gnonfin, Laure Gouba

The separability problem is one of the basic and emergent problems in the present and future quantum information processing. The latter focuses on information and computing based on quantum mechanics and uses quantum bits as its basic information units. In this paper, we present an overview of the progress in the separability problem in bipartite systems, more specifically in two quantum bits systems from the criterion based on the inequalities of Bell in $1964$ to the recent criteria of separability in 2018.

arXiv:2208.04747•Aug 1, 2022•0 citations

On the Separability Problem of Quantum Systems

Яхъяева Гульнара Эркиновна, Vladimir Kharchenko

When developing and operating quantum computers, it is necessary to be able to check quantum registers for the presence of quantum entanglement between its subsystems, due to which quantum computers gain computational advantage in solving many problems over classical computers. The state in which a quantum system consists of two or more subsystems that are not entangled with each other is called separable.In this article, we provide an overview of various existing approaches to solving the problem of determining separability in a quantum system. To do this, we provide an overview of works on this topic, describing both established and new approaches, highlighting directions in which new possibilities for solving the problem can be explored. We provide a definition of the problem of checking a system for separability, based on which we describe several applicable separability criteria. We provide a model-theoretic approach to solving the separability problem, describing a quantum system as a blurry model.

International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE)•Nov 14, 2025•0 citations

A decomposition method for the bipartite separability of bell diagonal states

Su Wei, Kuan Peng Chen, Ming-Chung Tsai +1 more

A new decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic inequality of the coefficients of a given Bell diagonal states and can be derived via a simple algorithmic calculation of its invariants. In addition, the criterion can be extended to a quantum system of higher dimension. Keywords—decomposition, bipartite separability, Bell diagonal states.

World academy of science, engineering and technology•Apr 1, 2011•0 citations

A Decomposition Method For The Bipartite Separability Of Bell Diagonal States

Wei-Chih Su, Kuan-Peng Chen, Ming-Chung Tsai +1 more

A new decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic inequality of the coefficients of a given Bell diagonal states and can be derived via a simple algorithmic calculation of its invariants. In addition, the criterion can be extended to a quantum system of higher dimension.

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering•Apr 24, 2011•0 citations

Separability Criterion of Bipartite Qubit States

BI Hong-mei

Generally,to decide a given quantum state to be entangled or not,or to be useful for quantum information processing purposes is a difficult question.In this note,the separability of quantum states in bipartite quantum systems is investigated.According to the analysis of the expanded form of density matrix in the separable quantum state and the relationship of expansion coefficient,a new separability criterion of bipartite quantum states is obtained: if a quantum state in a bipartite quantum system of arbitrary dimension is separable,the expansion coefficient satisfies certain inequality.This method requires only the dimensions of systems and the expansion coefficient of density matrix which can be easily got,and the computation is easy,so it has its application value.

Journal of Xi'an Technological University•Jan 1, 2008•0 citations

Characterizing the entanglement of bipartite quantum systems

Vittorio Giovannetti, Stefano Mancini, David Vitali +1 more

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.

arXiv:quant-ph/0210155•Physical Review A•Feb 28, 2003•208 citations
The separability problem is one of the basic and emergent problems in the present and future quantum information processing. The latter focuses on information and computing based on quantum mechanics and uses quantum bits as its basic information units. In this paper, we present an overview of the progress in the separability problem in bipartite systems, more specifically in two quantum bits systems from the criterion based on the inequalities of Bell in 196419641964 to the recent criteria of separability in 2018.
When developing and operating quantum computers, it is necessary to be able to check quantum registers for the presence of quantum entanglement between its subsystems, due to which quantum computers gain computational advantage in solving many problems over classical computers. The state in which a quantum system consists of two or more subsystems that are not entangled with each other is called separable.In this article, we provide an overview of various existing approaches to solving the problem of determining separability in a quantum system. To do this, we provide an overview of works on this topic, describing both established and new approaches, highlighting directions in which new possibilities for solving the problem can be explored. We provide a definition of the problem of checking a system for separability, based on which we describe several applicable separability criteria. We provide a model-theoretic approach to solving the separability problem, describing a quantum system as a blurry model.
Generally,to decide a given quantum state to be entangled or not,or to be useful for quantum information processing purposes is a difficult question.In this note,the separability of quantum states in bipartite quantum systems is investigated.According to the analysis of the expanded form of density matrix in the separable quantum state and the relationship of expansion coefficient,a new separability criterion of bipartite quantum states is obtained: if a quantum state in a bipartite quantum system of arbitrary dimension is separable,the expansion coefficient satisfies certain inequality.This method requires only the dimensions of systems and the expansion coefficient of density matrix which can be easily got,and the computation is easy,so it has its application value.