A unitary code is a finite subset of the unitary group in which a few inner product values occur between elements.
2.
Specifically, a unitary code is defined as a finite subset X \ subset U ( d ) if for all U \ neq M in X | tr ( U ^ * M ) | ^ 2 takes only distinct values.
3.
Observe that the space linearly spanned by the matrices U ^ { \ otimes r } \ otimes ( U ^ { * } ) ^ { \ otimes s } dU over all choices of U is identical to the restriction U \ in X and r + s = t This observation leads to a conclusion about the duality between unitary designs and unitary codes.
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