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

Minimal entanglement generating set for general pure multipartite states

Hoshang Heydari

Published Mar 16, 2006• 0 citations
OpenAlex

Abstract

We propose a minimal entanglement generating set for a general multipartite state based on concurrences classes. In particular, we construct concurrence for general three-partite states based on a redefinition of our concurrence classes. This shows that a measure of entanglement for three-partite states can be decomposed into two different classes that are constructed by two different local operators. Then based on this construction we introduce the minimal entanglement generating set for three-partite states. Moreover, we generalize our result to general multipartite states.

Related papers

Generating set for general multipartite entangled states

Hoshang Heydari

We propose a entanglement generating set for a general multipartite state based on the of concurrence. In particular, we show that concurrence for general multipartite states can be constructed by different classes of local operators which are defined by complement of positive operator valued measure on quantum phases. The entanglement generating set consists of different classes of entanglement that are detected by these classes of operators and contributes to the degree of entanglement for a general multipartite state.

arXiv:quant-ph/0603143•Mar 16, 2006•0 citations

Concurrence classes for general pure multipartite states

Hoshang Heydari

We propose concurrence classes for general pure multipartite states based on an orthogonal complement of a positive operator-valued measure on quantum phase. In particular, we construct W m class, GHZ m , and GHZ m −1 class concurrences for general pure m -partite states. We give explicit expressions for W 3 and GHZ 3 class concurrences for general pure three-partite states and for W 4 , GHZ 4 and GHZ 3 class concurrences for general pure four-partite states.

arXiv:quant-ph/0505109•Journal of Physics A Mathematical and General•Sep 21, 2005•7 citations

Concurrence for general multipartite states

Hoshang Heydari

We construct a generalized concurrence for general multipartite states based on local W-class and GHZ-class operators. We explicitly construct the corresponding concurrence for three-partite states. The construction of the concurrence is interesting since it is based on local operators and therefore gives some hints on the classification of multipartite states.

arXiv:quant-ph/0608224•Journal of Physics A Mathematical and General•Nov 21, 2006•6 citations

General pure multipartite entangled states and the Segre variety

Hoshang Heydari

We construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. This measure of entanglement works for any pure state and vanishes on multipartite product states. We give explicit expressions for general pure three-partite and four-partite states, and compare our measure of entanglement with the generalized concurrence.

arXiv:quant-ph/0603127•Journal of Physics A Mathematical and General•Jul 19, 2006•14 citations

DIFFERENT CLASSES OF QUANTUM GATES ENTANGLERS FOR MULTIPARTITE STATES

Hoshang Heydari

We construct quantum gates entanglers for different classes of multipartite states. In particular, we construct entangler operators for W and GHZ classes of multipartite states based on the construction of the concurrence classes. We also discuss in detail these two classes of the quantum gates entanglers for three-partite states.

International Journal of Quantum Information•Feb 1, 2009•1 citation

Multipartite entanglement and hyperdeterminants

Akimasa Miyake, Miki Wadati

We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively. Our approach reveals how inequivalent multipartite entangled classes of pure states constitute a partially ordered structure under local actions, significantly different from a totally ordered one in the bipartite case. Moreover, the generic entangled class of the maximal dimension, given by the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the \(n \!\geq\! 4\) qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical \(n\)-partite entangled states. Our classification is also useful for that of mixed states.

arXiv:quant-ph/0212146•Quantum Information and Computation•Nov 1, 2002•53 citations
We propose a minimal entanglement generating set for a general multipartite state based on concurrences classes. In particular, we construct concurrence for general three-partite states based on a redefinition of our concurrence classes. This shows that a measure of entanglement for three-partite states can be decomposed into two different classes that are constructed by two different local operators. Then based on this construction we introduce the minimal entanglement generating set for three-partite states. Moreover, we generalize our result to general multipartite states.
We propose a entanglement generating set for a general multipartite state based on the of concurrence. In particular, we show that concurrence for general multipartite states can be constructed by different classes of local operators which are defined by complement of positive operator valued measure on quantum phases. The entanglement generating set consists of different classes of entanglement that are detected by these classes of operators and contributes to the degree of entanglement for a general multipartite state.
We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively. Our approach reveals how inequivalent multipartite entangled classes of pure states constitute a partially ordered structure under local actions, significantly different from a totally ordered one in the bipartite case. Moreover, the generic entangled class of the maximal dimension, given by the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the n ⁣≥ ⁣4n \!\geq\! 4n≥4 qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical nnn-partite entangled states. Our classification is also useful for that of mixed states.