Algebraic measures of entanglement
| dc.creator | Brylinski, Jean-Luc | |
| dc.date | 2000-08-06 | |
| dc.date.accessioned | 2026-07-07T06:00:37Z | |
| dc.date.available | 2026-07-07T06:00:37Z | |
| dc.description | We study the rank of a general tensor $u$ in a tensor product $H_1\ot...\ot H_k$. The rank of $u$ is the minimal number $p$ of pure states $v_1,...,v_p$ such that $u$ is a linear combination of the $v_j$'s. This rank is an algebraic measure of the degree of entanglement of $u$. Motivated by quantum computation, we completely describe the rank of an arbitrary tensor in $(\C^2)^{\ot 3}$ and give normal forms for tensor states up to local unitary transformations. We also obtain partial results for $(\C^2)^{\ot 4}$; in particular, we show that the maximal rank of a tensor in $(\C^2)^{\ot 4}$ is equal to 4. | |
| dc.description | 10 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0008031 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0008031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/89013 | |
| dc.subject | Quantum Physics | |
| dc.title | Algebraic measures of entanglement | |
| dc.type | text |