Definition

Let G be a finite group of square order n^2.
A nice error basis is a set of unitary nxn matrices D(g) parametrized by the index group G such that

We only list the matrices corresponding to generators of the group G. The nice error bases for this index group G can be constructed as follows.

Then all unitary error bases with index group G are projectively equivalent to one of the bases constructed by the above method. Recall that two nice error bases D(g) and E(g) are said to be projectively equivalent if and only if there exists an invertible matrix T and a complex-valued function b such that

Notation: E(d) denotes a primitive d-th root of unity.

The following example illustrates the main points of this definition.


An entry from the Catalogue of Nice Error Bases, a joint project of Andreas Klappenecker and Martin Rötteler.
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