Article
Compact set of invariants characterizing graph states of up to eight qubits
Author/s | Cabello Quintero, Adán
![]() ![]() ![]() ![]() ![]() ![]() López Tarrida, Antonio José ![]() ![]() ![]() ![]() ![]() ![]() Moreno,, Pilar Portillo Fernández, José Ramón ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Física Aplicada II |
Publication Date | 2009 |
Deposit Date | 2022-07-29 |
Published in |
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Abstract | 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≥7. On ... 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≥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 2×1036 for n=7) to be practical. Here we solve the problem of deciding which entanglement class a graph state of n≤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≤8 qubits. |
Funding agencies | Junta de Andalucía Ministerio de Ciencia e Innovación (MICIN). España Ministerio de Educación y Ciencia (MEC). España |
Project ID. | P06-FQM-02243
![]() FIS2008-05596 ![]() PAI-FQM-0239 ![]() P06-FQM-01649 ![]() MTM2008-05866-C03-01 ![]() PAI-FQM-0164 ![]() |
Citation | Cabello Quintero, A., López Tarrida, A.J., Moreno, y Portillo Fernández, J.R. (2009). Compact set of invariants characterizing graph states of up to eight qubits. Physical Review A, 80 (1, art. nº 012102), 012102-1-012102-7. |
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