A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
IEEE Transactions on Information Theory , volume =
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Random dimension reduction replaces full dimension with max rank in sample complexity for symmetric quantum state properties and connects to but differs from random purification.
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Quantum Time Lower Bounds by Permutation Invariance
A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
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Random dimension reduction and learning symmetric properties of quantum states
Random dimension reduction replaces full dimension with max rank in sample complexity for symmetric quantum state properties and connects to but differs from random purification.