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/0611011

Genuine tripartite entanglement and quantum phase transition

Chang‐shui Yu, He‐Shan Song, H. T. Cui

Published Nov 1, 2006• 0 citations
arXivHTMLPDF

Abstract

A new formulation called as entanglement measure for simplification, is presented to characterize genuine tripartite entanglement of $(2\times 2\times n)-$dimensional quantum pure states. The formulation shows that the genuine tripartite entanglement can be described only on the basis of the local $(2\times 2)-$dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang (Phys. Rev. A \textbf{71}, 030302(R) (2005)) is reconsidered by employing the entanglement measure. The results show that a discontinuity in the first derivative of the entanglement measure or in the entanglement measure itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously prior to concurrence. Hence, the given entanglement measure may become a new alternate candidate to help study the connection between quantum entanglement and quantum phase transitions.

DOI
10.48550/arxiv.quant-ph/0611011

Related papers

Genuine tripartite entanglement and quantum phase transition

Chang‐shui Yu, He‐Shan Song, Cui Hai-Tao

A new simplified formula is presented to characterize genuine tripartite entanglement of (2 ⊗ 2 ⊗ n )-dimensional quantum pure states. The formula turns out equivalent to that given in ( Quant. Inf. Comp. 7 (7) 584 (2007)), hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local (2 ⊗ 2)-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang ( Phys. Rev. A 71 030302(R) (2005)) are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.

Chinese Physics B•Aug 1, 2008•2 citations

Genuine tripartite entanglement monotone of (2⊗2⊗n) -dimensional systems

Chang‐shui Yu, Ling Zhou, He‐Shan Song

A genuine tripartite entanglement monotone is presented for $(2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}n)$-dimensional tripartite pure states, obtained by introducing an entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin-$1/2$ chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.

arXiv:0802.1975•Physical Review A•Feb 13, 2008•12 citations

Existence Criterion of Genuine Tripartite Entanglement

Chang-shui Yu He-shan Song

In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits (Phys. Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states (Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.

arXiv:quant-ph/0603035•Mar 6, 2006•0 citations

Genuine tripartite entanglement semi-monotone for 2x2xn-dimensional systems

C.-S. Yu, H. S. Song, Y.-H. Wang

In this paper, we present a new approach to study genuine tripartite entanglement existing in $(2\times 2\times n)-$dimensional quantum pure states. By utilizing the approach, we introduce a particular quantity to measure genuine tripartite entanglement. The quantity is shown to be an entanglement monotone in 2-dimensional subsystems (semi-monotone) and reaches zero for separable states and $(2\times 2\times 2)-$dimensional $W$ states, hence is a good criterion to characterize genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximation technique. As applications, we give the analytic approximation for weakly mixed states, and study the genuine tripartite entanglement of two given weakly mixed states.

arXiv:quant-ph/0607032•Quantum Information and Computation•Sep 1, 2007•7 citations

Genuine multipartite entanglement in the cluster-Ising model

S. M. Giampaolo, Beatrix C. Hiesmayr

We evaluate and analyze the exact value of a measure for local genuine tripartite entanglement in the one-dimensional cluster-Ising model for spin- particles. This model is attractive since cluster states are considered to be relevant sources for applying quantum algorithms and the model is experimentally feasible. Whereas bipartite entanglement is identically vanishing, we find that genuine tripartite entanglement is non zero in the anti-ferromagnetic phase and also in the cluster phase well before the critical point. We prove that the measure of local genuine tripartite entanglement captures all the properties of the symmetry-protected topological quantum phase transition. Remarkably, we find that the amount of genuine tripartite entanglement is independent of whether the ground states satisfy or break the symmetries of the Hamiltonian. We provide also strong evidences that local genuine tripartite entanglement represents the unique non-vanishing genuine multipartite entanglement.

arXiv:1403.7184•New Journal of Physics•Sep 24, 2014•47 citations

Existence criterion of genuine tripartite entanglement

Chang‐shui Yu, He‐Shan Song

In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the Kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.

arXiv:0812.5009•Physical Review A•Mar 17, 2006•8 citations
A new formulation called as entanglement measure for simplification, is presented to characterize genuine tripartite entanglement of (2×2×n)−(2\times 2\times n)-(2×2×n)−dimensional quantum pure states. The formulation shows that the genuine tripartite entanglement can be described only on the basis of the local (2×2)−(2\times 2)-(2×2)−dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang (Phys. Rev. A \textbf{71}, 030302(R) (2005)) is reconsidered by employing the entanglement measure. The results show that a discontinuity in the first derivative of the entanglement measure or in the entanglement measure itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously prior to concurrence. Hence, the given entanglement measure may become a new alternate candidate to help study the connection between quantum entanglement and quantum phase transitions.
A new simplified formula is presented to characterize genuine tripartite entanglement of (2 ⊗ 2 ⊗ n )-dimensional quantum pure states. The formula turns out equivalent to that given in ( Quant. Inf. Comp. 7 (7) 584 (2007)), hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local (2 ⊗ 2)-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang ( Phys. Rev. A 71 030302(R) (2005)) are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.
A genuine tripartite entanglement monotone is presented for $(2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}n)$-dimensional tripartite pure states, obtained by introducing an entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin-1/21/21/2 chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits (Phys. Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states (Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.
In this paper, we present a new approach to study genuine tripartite entanglement existing in (2×2×n)−(2\times 2\times n)-(2×2×n)−dimensional quantum pure states. By utilizing the approach, we introduce a particular quantity to measure genuine tripartite entanglement. The quantity is shown to be an entanglement monotone in 2-dimensional subsystems (semi-monotone) and reaches zero for separable states and (2×2×2)−(2\times 2\times 2)-(2×2×2)−dimensional WWW states, hence is a good criterion to characterize genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximation technique. As applications, we give the analytic approximation for weakly mixed states, and study the genuine tripartite entanglement of two given weakly mixed states.
We evaluate and analyze the exact value of a measure for local genuine tripartite entanglement in the one-dimensional cluster-Ising model for spin- particles. This model is attractive since cluster states are considered to be relevant sources for applying quantum algorithms and the model is experimentally feasible. Whereas bipartite entanglement is identically vanishing, we find that genuine tripartite entanglement is non zero in the anti-ferromagnetic phase and also in the cluster phase well before the critical point. We prove that the measure of local genuine tripartite entanglement captures all the properties of the symmetry-protected topological quantum phase transition. Remarkably, we find that the amount of genuine tripartite entanglement is independent of whether the ground states satisfy or break the symmetries of the Hamiltonian. We provide also strong evidences that local genuine tripartite entanglement represents the unique non-vanishing genuine multipartite entanglement.
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the Kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.