On polynomial invariants of several qubits
| dc.creator | Osterloh, Andreas | |
| dc.creator | Djokovic, Dragomir Z. | |
| dc.date | 2008-04-10 | |
| dc.date | 2009-02-17 | |
| dc.date.accessioned | 2026-07-07T12:59:57Z | |
| dc.date.available | 2026-07-07T12:59:57Z | |
| dc.description | It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the $SL^*$ invariants, we analyze the $SL(2,\CC)$-invariants of four resp. five qubits and decompose them into irreducible modules for the symmetric group $S_4$ resp. $S_5$ of qubit permutations. A classifying set of measures of genuine multipartite entanglement is given by the ideal of the algebra of $SL^*$-invariants vanishing on arbitrary product states. We find that low degree homogeneous components of this ideal can be constructed in full by using the approach introduced in [Phys. Rev. A 72, 012337 (2005)]. Our analysis highlights an intimate connection between this latter procedure and the standard methods to create invariants, such as the $Ω$-process. As the degrees of invariants increase, the alternative method proves to be particularly efficient. | |
| dc.description | 29 pages, 3 eps figures, aipproc. Minor modifications and corrections. Length change only due to style change | |
| dc.identifier | https://arxiv.org/abs/0804.1661 | |
| dc.identifier | http://arxiv.org/abs/0804.1661 | |
| dc.identifier | J. Math. Phys. 50, 033509 (2009). | |
| dc.identifier | doi:10.1063/1.3075830 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225729 | |
| dc.subject | Quantum Physics | |
| dc.title | On polynomial invariants of several qubits | |
| dc.type | text |