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Unitary designs and codes · Around

2008

Unitary designs and codes

Roy, Aidan, Scott, A. J.

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A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere.

In this paper, we use irreducible representations of the unitary group to find a general lower bound on the size of a unitary t-design in U(d), for any d and t.
We also introduce the notion of a unitary code - a subset of U(d) in which the trace inner product of any pair of matrices is restricted to only a small number of distinct values - and give an upper bound for the size of a code of degree s in U(d) for any d and s.
These bounds can be strengthened when the particular inner product values that occur in the code or design are known.

Built on

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1973
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G. Benkart, M. Chakrabarti, T. Halverson, R. Leduc, C. Lee, and J. Stroomer
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