Efficient 2-designs from bases exist
| dc.creator | McConnell, Gary | |
| dc.creator | Gross, David | |
| dc.date | 2007-10-08 | |
| dc.date.accessioned | 2026-07-07T09:39:16Z | |
| dc.date.available | 2026-07-07T09:39:16Z | |
| dc.description | We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications in quantum information theory (e.g. in state tomography, cloning, or cryptography) -- however it is suspected that maximal sets exist only in prime-power dimensions. Our construction offers an efficient alternative for general dimensions. The findings are based on a framework recently established in [A. Roy and A. Scott, J. Math. Phys. 48, 072110 (2007)], which reduces the construction of such bases to the combinatorial problem of finding certain highly nonlinear functions between abelian groups. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/0710.1502 | |
| dc.identifier | http://arxiv.org/abs/0710.1502 | |
| dc.identifier | Quantum Inf. Comput. 8, 734 (2008) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161108 | |
| dc.subject | Quantum Physics | |
| dc.title | Efficient 2-designs from bases exist | |
| dc.type | text |