Efficient 2-designs from bases exist

Details Efficient 2-designs from bases exist Efficient 2-designs from bases exist

2007-10-08

arxiv.org/abs/0710.1502v1

Quantum Inf. Comput. 8, 734 (2008)

Physics

Quantum Physics

5 pages

Scientific paper

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.

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