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

International ICST Conference on Communications and Networking in China

Entanglement of 9-qubit graph states

Sui Yan, Xiaoyu Chen

Published Jan 1, 2010• 0 citations
Publisher

Abstract

The entanglement of graph states can be calculated by adopting Iterative algorithm. The number of inequivalent classes of 9-qubit graph states is 440. All 440 local inequivalent graphs are classified as two categories: graphs with equal upper LOCC entanglement bound and lower bipartite entanglement
DOI
10.4108/chinacom.2010.80

Related papers

Entanglement of 10-qubit graph states

Guowei Chen, Xiaoyu Chen

The number of inequivalent classes of 10-qubit graph states is 3132. All 3132 local inequivalent graphs are classified as two categories: graphs with equal bound, graphs with unequal bounds. We will use different methods to calculate the entanglement of graph states of ten qubits for the different categories. For graph states with different entanglement bounds, the closest product states are given, and they have different structural characters.

International Conference on Natural Computation (ICNC)•Aug 1, 2010•0 citations

Entanglement of graph states up to eight qubits

Xiaoyu Chen

The entanglement of graph states up to eight qubits is calculated in the regime of iteration calculation. The entanglement measures could be the relative entropy of entanglement, the logarithmic robustness or the geometric measure. All 146 local inequivalent graphs are classified as two categories: graphs with identical upper LOCC entanglement bound and lower bipartite entanglement bound, graphs with unequal bounds. The late may displays non-integer entanglement. The precision of iteration calculation of the entanglement is less than $10^{-14}$.

arXiv:0909.1603•Journal of Physics B Atomic Molecular and Optical Physics•Apr 6, 2010•13 citations

Entanglement of Graph Qutrit States

Haitao Li, Xiaoyu Chen

The number of inequivalent classes of up to 8-qutrit graph states is 1002, with 239 decomposable graphs and 763 indecomposable graphs. Apparently, the former can be decomposed to several indecomposable parts. For qubit graph states, the upper and lower bounds of entanglement have been given. If the two bounds don't coincide, the entanglement can be calculated by iterative method. For qutrit graph states, their lower bounds can be found through the local complementation operations. But its hard to find the upper bound because the qutrit graph states have 2 basis states which are GHZ state and W state. Fortunately, the iterative method can also be used here. In this paper, we calculated the entanglement of all the 1002 graph states. Through researching the results, we found the similar feature with graph qubit states that the decimal part of entanglement is stable.

International Conference on Intelligence Science and Information Engineering•Aug 1, 2011•3 citations

Entanglement and Closest Product States of Graph States with 9 to 11 Qubits

Cuifeng Wang, Li-zhen Jiang, Lei Wang

The numbers of local complimentary inequivalent graph states for 9, 10 and 11 qubit systems are 440, 3132, 40457, respectively. We calculate the entanglement, the lower and upper bounds of the entanglement and obtain the closest product states for all these graph states. New patterns of closest product states are analyzed.

Journal of Applied Mathematics and Physics•Jan 1, 2013•2 citations

Compact set of invariants characterizing graph states of up to eight qubits

Adán Cabello, Antonio J. López-Tarrida, Pilar Moreno +1 more

The set of entanglement measures proposed by Hein, Eisert, and Briegel for $n$-qubit graph states [Phys. Rev. A 69, 062311 (2004)] fails to distinguish between inequivalent classes under local Clifford operations if $n\ensuremath{\ge}7$. On the other hand, the set of invariants proposed by van den Nest, Dehaene, and De Moor (VDD) [Phys. Rev. A 72, 014307 (2005)] distinguishes between inequivalent classes, but contains too many invariants (more than $2\ifmmode\times\else\texttimes\fi{}{10}^{36}$ for $n=7$) to be practical. Here we solve the problem of deciding which entanglement class a graph state of $n\ensuremath{\le}8$ qubits belongs to by calculating some of the state's intrinsic properties. We show that four invariants related to those proposed by VDD are enough for distinguishing between all inequivalent classes with $n\ensuremath{\le}8$ qubits.

arXiv:0904.3551•Physical Review A•Jul 1, 2009•13 citations

Calculation of entanglement in graph states up to five-qubit based on generalized concurrence

Ahmad Akhound, Saeed Haddadi, Mohammad Ali Chaman Motlagh

We propose a new classification for the entanglement in graph states based on generalized con- currence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in five categories and 1024 five-qubit graph states are in ten classes. We also compare this classification with equivalence classes of these graph states under local complementation (LC) operator, and the obtained result suggests that classification by generalized concurrence is not in contradiction with the LC-rule.

arXiv:1610.02560•Oct 8, 2016•0 citations
The entanglement of graph states up to eight qubits is calculated in the regime of iteration calculation. The entanglement measures could be the relative entropy of entanglement, the logarithmic robustness or the geometric measure. All 146 local inequivalent graphs are classified as two categories: graphs with identical upper LOCC entanglement bound and lower bipartite entanglement bound, graphs with unequal bounds. The late may displays non-integer entanglement. The precision of iteration calculation of the entanglement is less than 10−1410^{-14}10−14.
The number of inequivalent classes of up to 8-qutrit graph states is 1002, with 239 decomposable graphs and 763 indecomposable graphs. Apparently, the former can be decomposed to several indecomposable parts. For qubit graph states, the upper and lower bounds of entanglement have been given. If the two bounds don't coincide, the entanglement can be calculated by iterative method. For qutrit graph states, their lower bounds can be found through the local complementation operations. But its hard to find the upper bound because the qutrit graph states have 2 basis states which are GHZ state and W state. Fortunately, the iterative method can also be used here. In this paper, we calculated the entanglement of all the 1002 graph states. Through researching the results, we found the similar feature with graph qubit states that the decimal part of entanglement is stable.
The set of entanglement measures proposed by Hein, Eisert, and Briegel for nnn-qubit graph states [Phys. Rev. A 69, 062311 (2004)] fails to distinguish between inequivalent classes under local Clifford operations if $n\ensuremath{\ge}7$. On the other hand, the set of invariants proposed by van den Nest, Dehaene, and De Moor (VDD) [Phys. Rev. A 72, 014307 (2005)] distinguishes between inequivalent classes, but contains too many invariants (more than $2\ifmmode\times\else\texttimes\fi{}{10}^{36}$ for n=7n=7n=7) to be practical. Here we solve the problem of deciding which entanglement class a graph state of $n\ensuremath{\le}8$ qubits belongs to by calculating some of the state's intrinsic properties. We show that four invariants related to those proposed by VDD are enough for distinguishing between all inequivalent classes with $n\ensuremath{\le}8$ qubits.
We propose a new classification for the entanglement in graph states based on generalized con- currence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in five categories and 1024 five-qubit graph states are in ten classes. We also compare this classification with equivalence classes of these graph states under local complementation (LC) operator, and the obtained result suggests that classification by generalized concurrence is not in contradiction with the LC-rule.