Quantum-inspired estimators for F_alpha(P) and F_alpha(rho) achieve optimal sample complexity n ~ alpha and minimax MSE rate alpha/n, improving prior O(alpha^2) bounds.
Quantum State Certification , booktitle =
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A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
Unconditional lower bounds and matching (or nearly matching) upper bounds are proved for public- and private-coin distributed quantum state certification under joint classical-plus-quantum communication limits.
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.
Adding loop composition to branching quantum walk models produces a variable-time quantum search algorithm whose complexity matches the best known results.
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Towards Minimax Estimation of High-Order Functionals by Quantum Arguments
Quantum-inspired estimators for F_alpha(P) and F_alpha(rho) achieve optimal sample complexity n ~ alpha and minimax MSE rate alpha/n, improving prior O(alpha^2) bounds.
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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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Distributed Property Testing with (Quantum) Carrier Pigeons: Tight Bounds on State Certification
Unconditional lower bounds and matching (or nearly matching) upper bounds are proved for public- and private-coin distributed quantum state certification under joint classical-plus-quantum communication limits.
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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.
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Loop Composition in Quantum Algorithms
Adding loop composition to branching quantum walk models produces a variable-time quantum search algorithm whose complexity matches the best known results.