We prove our lower bounds using a new quantum analogue of the Ingster-Suslina method. Essentially, we find a convenient way to decompose the quantum χ^2 divergence between a mixture of states and a fixed reference state.

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New work with @booleananalysis.bsky.social! We prove instance-optimal bounds for quantum state certification when testers can measure all copies simultaneously, finding that the optimal copy complexity depends on how close to maximally mixed the hypothesis state is.

arxiv.org/abs/2507.06010

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