dorsal/arxiv
View SchemaEntangling Power of Permutations
| Authors | Lieven Clarisse, Sibasish Ghosh, Simone Severini, Anthony Sudbery |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502040 |
| URL | https://arxiv.org/abs/quant-ph/0502040 |
| DOI | 10.1103/PhysRevA.72.012314 |
| Journal | Phys. Rev. A 72, 012314 (2005) |
Abstract
The notion of entangling power of unitary matrices was introduced by Zanardi, Zalka and Faoro [PRA, 62, 030301]. We study the entangling power of permutations, given in terms of a combinatorial formula. We show that the permutation matrices with zero entangling power are, up to local unitaries, the identity and the swap. We construct the permutations with the minimum nonzero entangling power for every dimension. With the use of orthogonal latin squares, we construct the permutations with the maximum entangling power for every dimension. Moreover, we show that the value obtained is maximum over all unitaries of the same dimension, with possible exception for 36. Our result enables us to construct generic examples of 4-qudits maximally entangled states for all dimensions except for 2 and 6. We numerically classify, according to their entangling power, the permutation matrices of dimension 4 and 9, and we give some estimates for higher dimensions.
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"abstract": "The notion of entangling power of unitary matrices was introduced by Zanardi,\nZalka and Faoro [PRA, 62, 030301]. We study the entangling power of\npermutations, given in terms of a combinatorial formula. We show that the\npermutation matrices with zero entangling power are, up to local unitaries, the\nidentity and the swap. We construct the permutations with the minimum nonzero\nentangling power for every dimension. With the use of orthogonal latin squares,\nwe construct the permutations with the maximum entangling power for every\ndimension. Moreover, we show that the value obtained is maximum over all\nunitaries of the same dimension, with possible exception for 36. Our result\nenables us to construct generic examples of 4-qudits maximally entangled states\nfor all dimensions except for 2 and 6. We numerically classify, according to\ntheir entangling power, the permutation matrices of dimension 4 and 9, and we\ngive some estimates for higher dimensions.",
"arxiv_id": "quant-ph/0502040",
"authors": [
"Lieven Clarisse",
"Sibasish Ghosh",
"Simone Severini",
"Anthony Sudbery"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.012314",
"journal_ref": "Phys. Rev. A 72, 012314 (2005)",
"title": "Entangling Power of Permutations",
"url": "https://arxiv.org/abs/quant-ph/0502040"
},
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