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

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering

A Decomposition Method For The Bipartite Separability Of Bell Diagonal States

Wei-Chih Su, Kuan-Peng Chen, Ming-Chung Tsai, Zheng-Yao Su

Published Apr 24, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.1055834

Related papers

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 Criterion for the Bipartite Separability of Bell Diagonal States

Ming-Chung Tsai, Po-Chung Chen, Wei-Chi Su +1 more

A 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 form 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.

arXiv:1310.7511•Oct 28, 2013•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

AN EFFICIENT SEPARABILITY CRITERION FOR n-PARTITE ARBITRARILY DIMENSIONAL QUANTUM STATES

Yinxiang Long, Daowen Qiu, Dongyang Long

In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.

International Journal of Quantum Information•Jun 1, 2011•0 citations

The Separability Problem in Two Qubits Revisited

Honorine Gnonfin, Laure Gouba

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.

Symmetry•Nov 20, 2023•4 citations

Finding a maximally correlated state: Simultaneous Schmidt decomposition of bipartite pure states

Tohya Hiroshima, Masahito Hayashi

We consider a bipartite mixed state of the form $\ensuremath{\rho}={\ensuremath{\sum}}_{\ensuremath{\alpha},\ensuremath{\beta}=1}^{l}{a}_{\ensuremath{\alpha}\ensuremath{\beta}}\ensuremath{\mid}{\ensuremath{\psi}}_{\ensuremath{\alpha}}⟩⟨{\ensuremath{\psi}}_{\ensuremath{\beta}}⟩$, where $\ensuremath{\mid}{\ensuremath{\psi}}_{\ensuremath{\alpha}}⟩$ are normalized bipartite state vectors, and matrix $({a}_{\ensuremath{\alpha}\ensuremath{\beta}})$ is positive semidefinite. We provide a necessary and sufficient condition for the state $\ensuremath{\rho}$ taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of $\ensuremath{\mid}{\ensuremath{\psi}}_{\ensuremath{\alpha}}⟩$ for $\ensuremath{\alpha}=1,2,\dots{},l$. Using this criterion, we can judge completely whether or not the state $\ensuremath{\rho}$ is equivalent to the maximally correlated state, in which the distillable entanglement is given by a simple formula. For generalized Bell states, this criterion is written as a simple algebraic relation between indices of the states. We also discuss the local distinguishability of the generalized Bell states that are simultaneously Schmidt decomposable.

arXiv:quant-ph/0405107•Physical Review A•Sep 22, 2004•30 citations
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.
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.
In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.
We consider a bipartite mixed state of the form $\ensuremath{\rho}={\ensuremath{\sum}}_{\ensuremath{\alpha},\ensuremath{\beta}=1}^{l}{a}_{\ensuremath{\alpha}\ensuremath{\beta}}\ensuremath{\mid}{\ensuremath{\psi}}_{\ensuremath{\alpha}}⟩⟨{\ensuremath{\psi}}_{\ensuremath{\beta}}⟩$, where $\ensuremath{\mid}{\ensuremath{\psi}}_{\ensuremath{\alpha}}⟩$ are normalized bipartite state vectors, and matrix $({a}_{\ensuremath{\alpha}\ensuremath{\beta}})$ is positive semidefinite. We provide a necessary and sufficient condition for the state $\ensuremath{\rho}$ taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of $\ensuremath{\mid}{\ensuremath{\psi}}_{\ensuremath{\alpha}}⟩$ for $\ensuremath{\alpha}=1,2,\dots{},l$. Using this criterion, we can judge completely whether or not the state $\ensuremath{\rho}$ is equivalent to the maximally correlated state, in which the distillable entanglement is given by a simple formula. For generalized Bell states, this criterion is written as a simple algebraic relation between indices of the states. We also discuss the local distinguishability of the generalized Bell states that are simultaneously Schmidt decomposable.