A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
Childs, Aram W
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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.
Computational constraints exponentially suppress accessible entanglement for some highly entangled quantum states and can make mixed-state min-entropy appear maximal when the information-theoretic version is negative.
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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.
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Accessible Quantum Correlations Under Complexity Constraints
Computational constraints exponentially suppress accessible entanglement for some highly entangled quantum states and can make mixed-state min-entropy appear maximal when the information-theoretic version is negative.