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

Quantum Information Processing

Entanglement measure for pure six-qubit quantum states

João Luzeilton de Oliveira, David Sena Oliveira, Rubens Viana Ramos

Published May 19, 2011• 3 citations
Publisher
DOI
10.1007/s11128-011-0248-8

Related papers

Cálculo do entrelaçamento de estados puros com quatro a seis qubits

David Sena Oliveira

This thesis is divided in three parts. The first one brings a brief review of the basic concepts about entanglement of quantum states with two and multiple qubits, including the entanglement monotones and the Groverian entanglement measure, which is calculated by a genetic algorithm. The second part is focused on the generation of a entanglement measures that identify only four qubit states with genuine entanglement. Some examples of the calculus of the entanglement of four qubit states, using the proposed measure, when these states are processed by quantum circuits, are presented. In the third part, the proposed measure is extended, to calculate the genuine entanglement of pure six qubits quantum states. Numerical simulations were realized aiming to show the variation, creation and annihilation of the entanglement of pure six qubits states.

•Jan 1, 2012•0 citations

Measures of Quantum Entanglement

P. K. Aravind

Springer eBooks•Jan 1, 1996•2 citations

Algebraic tools for the study of quantum entanglement

João Luzeilton de Oliveira

This thesis presents some results about two important subjects of the quantum information theory: quantum entanglement and quantum algorithms. Regarding the entanglement, a relationship between negativity and minors principals of Hermitian matrices was stablished, allowing the analysis of the entanglement of two qubits states, three and four qubits pure states, using the minors principals. It was also proposed a new measure, using negativity, for calculating the entanglement of pure states of six qubits. Finally, with respect to quantum algorithms it was proposed a quantum search algorithm able to finding the minimum of a function by performing only one measurement. The algorithm is described and an example of its usage in the calculation of the period of a periodic function is presented.

•Jan 1, 2012•0 citations

Quantum entanglement in multi-qubit systems

최정운

•Jan 1, 2004•0 citations

Quantification of multipartite entanglement with the use of LOCC transformation

Hiroyasu Tajima

Entanglement is known to be a promising resource which enables us to execute various quantum tasks. Its quantification has been successful for bipartite pure states. However, the quantification of entanglement for multipartite states has been in a difficult situation. The difficulty is due to the difference of structures between bipartite and multipartite states. In the present thesis, we introduce a new approach for this problem. We give a necessary and sufficient condition of the possibility of a deterministic LOCC transformation of three-qubit pure states. This condition is expressed as a transformation law of six entanglement parameters jAB, jAC , jBC , jABC , J5 and Qe, where jAB, jAC and jBC are bipartite entanglements, jABC is a tripartite entanglement, J5 is a tripartite parameter which means a kind of phase, and Qe is a new tripartite parameter which means a kind of charge. This fact shows that three-qubit pure states are a partially ordered set parametrized by the six entanglement parameters. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen’s work [14] to three-qubit pure states. We also clarify the rules of transfer and dissipation of entanglement. These rules guarantee that the tripartite entanglement can be transformed into bipartite entanglements, but that the bipartite entanglements cannot be transformed into the tripartite entanglement. This implies that the tripartite entanglement is a higher entity than the bipartite entanglements. With a new combination of the six entanglement parameters, the present condition can be simplified enough to determine easily whether a deterministic LOCC transformation from an arbitrary state |ψ〉 to another arbitrary state |ψ′〉 is possible or not. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation is given. This is an extension of Horodecki et al.’s work [24] to three-qubit pure states.

•Jan 1, 2012•0 citations

Robust entanglement measure for mixed quantum states

Dharmaraj Ramachandran, Aditya Dubey, Subrahmanyam S. G. Mantha +1 more

arXiv:2412.08304•Quantum Information Processing•Jul 31, 2025•2 citations
This thesis is divided in three parts. The first one brings a brief review of the basic concepts about entanglement of quantum states with two and multiple qubits, including the entanglement monotones and the Groverian entanglement measure, which is calculated by a genetic algorithm. The second part is focused on the generation of a entanglement measures that identify only four qubit states with genuine entanglement. Some examples of the calculus of the entanglement of four qubit states, using the proposed measure, when these states are processed by quantum circuits, are presented. In the third part, the proposed measure is extended, to calculate the genuine entanglement of pure six qubits quantum states. Numerical simulations were realized aiming to show the variation, creation and annihilation of the entanglement of pure six qubits states.
This thesis presents some results about two important subjects of the quantum information theory: quantum entanglement and quantum algorithms. Regarding the entanglement, a relationship between negativity and minors principals of Hermitian matrices was stablished, allowing the analysis of the entanglement of two qubits states, three and four qubits pure states, using the minors principals. It was also proposed a new measure, using negativity, for calculating the entanglement of pure states of six qubits. Finally, with respect to quantum algorithms it was proposed a quantum search algorithm able to finding the minimum of a function by performing only one measurement. The algorithm is described and an example of its usage in the calculation of the period of a periodic function is presented.
Entanglement is known to be a promising resource which enables us to execute various quantum tasks. Its quantification has been successful for bipartite pure states. However, the quantification of entanglement for multipartite states has been in a difficult situation. The difficulty is due to the difference of structures between bipartite and multipartite states. In the present thesis, we introduce a new approach for this problem. We give a necessary and sufficient condition of the possibility of a deterministic LOCC transformation of three-qubit pure states. This condition is expressed as a transformation law of six entanglement parameters jAB, jAC , jBC , jABC , J5 and Qe, where jAB, jAC and jBC are bipartite entanglements, jABC is a tripartite entanglement, J5 is a tripartite parameter which means a kind of phase, and Qe is a new tripartite parameter which means a kind of charge. This fact shows that three-qubit pure states are a partially ordered set parametrized by the six entanglement parameters. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen’s work [14] to three-qubit pure states. We also clarify the rules of transfer and dissipation of entanglement. These rules guarantee that the tripartite entanglement can be transformed into bipartite entanglements, but that the bipartite entanglements cannot be transformed into the tripartite entanglement. This implies that the tripartite entanglement is a higher entity than the bipartite entanglements. With a new combination of the six entanglement parameters, the present condition can be simplified enough to determine easily whether a deterministic LOCC transformation from an arbitrary state |ψ〉 to another arbitrary state |ψ′〉 is possible or not. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation is given. This is an extension of Horodecki et al.’s work [24] to three-qubit pure states.