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The most familiar witness-preserving amplification for QMA is based on Jordan's lemma and uses the projections $\Pi_1$ and $\Pi_2$ where $\Pi_1$ is he projection on the 'ancilla zero' space, and $\Pi_2$ is the projection on the space of accepted states by the original Arthur (for the full proof, read here).

My question is how can I prove the witness-preserving amplification theorem for QMA, using phase estimation of $e^{i\Pi_1\Pi_2\Pi_1}$ ?

I know it is possible (otherwise, it wouldn't be a question in the HW assignment I have received), but I just can't find the solution.

Any help or reference to a helpful source would be appreciated

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  • $\begingroup$ Can you make your question more precise? What do you mean by prove the witness preserving amplification using phase estimation of $e^{i\Pi_1 \Pi_2 \Pi_1}$? $\endgroup$
    – Chaithanya
    Oct 11, 2022 at 2:27

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