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Let $H$ be a hidden subgroup of $G_1$ that is indistinguishable from subgroup $H^{\prime}$ by quantum Fourier sampling. Now take a larger group $G_2$ such that it contains $G_1$. Now if I do quantum Fourier sampling over $G_2$ instead of $G_1$ are they still indistinguishable?

M. Al Jumaily
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