Entangling power of permutations

Journal Article · Fri Jul 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.012314· OSTI ID:20718322

Clarisse, Lieven; Sudbery, Anthony ^[1]; Ghosh, Sibasish ^[2]; Severini, Simone ^[1]

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1. Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)
2. Department of Computer Science, University of York, Heslington, York YO10 5DD (United Kingdom)

The notion of entangling power of unitary matrices was introduced by Zanardi et al., [Phys. Rev. A 62, 030301 (2000)]. 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 a possible exception for 36. Our result enables us to construct generic examples of 4-qudit maximally entangled states for all dimensions except for 2 and 6. We numerically classify, according to their entangling power, the permutation matrices of dimensions 4 and 9, and we give some estimates for higher dimensions.

• OSTI ID: 20718322
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

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