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

Neurocomputing

Geometric measures of entanglement in multipartite pure states via complex-valued neural networks

Maolin Che, Liqun Qi, Yimin Wei, Guofeng Zhang

Published Jun 19, 2018• 26 citations
Publisher
DOI
10.1016/j.neucom.2018.05.094

Related papers

Computing the geometric measure of entanglement of multipartite pure states by means of non-negative tensors

Shenglong Hu, Liqun Qi, Guofeng Zhang

The geometric measure of entanglement for pure states has attracted much attention. On the other hand, the spectral theory of non-negative tensors (hypermatrices) has been developed rapidly. In this paper, we show how the spectral theory of non-negative tensors can be applied to the study of the geometric measure of entanglement for pure states. For symmetric pure multipartite qubit or qutrit states an elimination method is given. For symmetric pure multipartite qudit states, a numerical algorithm with randomization is presented. We also show that a nonsymmetric pure state can be augmented to a symmetric one whose amplitudes can be encoded in a non-negative symmetric tensor, so the geometric measure of entanglement can be calculated. Several examples, such as $m\mathrm{GHZ}$ states, $W$ states, inverted $W$ states, qudits, and nonsymmetric states, are used to demonstrate the power of the proposed methods. Given a pure state, one can always find a change of basis (a unitary transformation) so that all the probability amplitudes of the pure state are non-negative under the new basis. Therefore, the methods proposed here can be applied to a very wide class of multipartite pure states.

Physical Review A•Jan 6, 2016•52 citations

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

Peiyuan Teng

arXiv:1609.02076•Quantum Information Processing•Jun 12, 2017•12 citations

The geometric measure of multipartite entanglement and the singular values of a hypermatrix

Joseph J. Hilling, Anthony Sudbery

It is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation, generalizing the singular-value equation of the matrix of coefficients of a bipartite state. The equation is solved for a class of three-qubit states.

arXiv:0905.2094•Journal of Mathematical Physics•Jul 1, 2010•53 citations

Entanglement Detection with Complex-Valued Neural Networks

Yue-Di Qu, Ruiqi Zhang, Shu‐Qian Shen +2 more

International Journal of Theoretical Physics•Sep 14, 2023•6 citations

The geometric measure of entanglement of pure states with nonnegative amplitudes and the spectral theory of nonnegative tensors

Shenglong Hu, Liqun Qi, Guofeng Zhang

The geometric measure of entanglement for a symmetric pure state with nonnegative amplitudes has attracted much attention. On the other hand, the spectral theory of nonnegative tensors (hypermatrices) has been developed rapidly. In this paper, we show how the spectral theory of nonnegative tensors can be applied to the study of the geometric measure of entanglement for a pure state with nonnegative amplitudes. Especially, an elimination method for computing the geometric measure of entanglement for symmetric pure multipartite qubit or qutrit states with nonnegative amplitudes is given. For symmetric pure multipartite qudit states with nonnegative amplitudes, a numerical algorithm with randomization is presented and proven to be convergent. We show that for the geometric measure of entanglement for pure states with nonnegative amplitudes, the nonsymmetric ones can be converted to the symmetric ones.

arXiv:1203.3675•Mar 16, 2012•15 citations

Geometric multipartite entanglement measures

Gerardo A. Paz-Silva, John Henry Reina

arXiv:quant-ph/0603102•Physics Letters A•Jan 9, 2007•4 citations
The geometric measure of entanglement for pure states has attracted much attention. On the other hand, the spectral theory of non-negative tensors (hypermatrices) has been developed rapidly. In this paper, we show how the spectral theory of non-negative tensors can be applied to the study of the geometric measure of entanglement for pure states. For symmetric pure multipartite qubit or qutrit states an elimination method is given. For symmetric pure multipartite qudit states, a numerical algorithm with randomization is presented. We also show that a nonsymmetric pure state can be augmented to a symmetric one whose amplitudes can be encoded in a non-negative symmetric tensor, so the geometric measure of entanglement can be calculated. Several examples, such as mGHZm\mathrm{GHZ}mGHZ states, WWW states, inverted WWW states, qudits, and nonsymmetric states, are used to demonstrate the power of the proposed methods. Given a pure state, one can always find a change of basis (a unitary transformation) so that all the probability amplitudes of the pure state are non-negative under the new basis. Therefore, the methods proposed here can be applied to a very wide class of multipartite pure states.
The geometric measure of entanglement for a symmetric pure state with nonnegative amplitudes has attracted much attention. On the other hand, the spectral theory of nonnegative tensors (hypermatrices) has been developed rapidly. In this paper, we show how the spectral theory of nonnegative tensors can be applied to the study of the geometric measure of entanglement for a pure state with nonnegative amplitudes. Especially, an elimination method for computing the geometric measure of entanglement for symmetric pure multipartite qubit or qutrit states with nonnegative amplitudes is given. For symmetric pure multipartite qudit states with nonnegative amplitudes, a numerical algorithm with randomization is presented and proven to be convergent. We show that for the geometric measure of entanglement for pure states with nonnegative amplitudes, the nonsymmetric ones can be converted to the symmetric ones.