Coherent quantum inference achieves O(1/ε) sample complexity for d-dimensional quantum purity amplification, exponentially better than the Ω(d/ε) required by any incoherent measurement-mediated protocol.
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Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.
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An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
Coherent quantum inference achieves O(1/ε) sample complexity for d-dimensional quantum purity amplification, exponentially better than the Ω(d/ε) required by any incoherent measurement-mediated protocol.
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Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs
Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.