A quantum estimator achieves near-optimal query complexity for integer-order Tsallis entropy, and the same technique yields a new information-theoretic proof that approximating x^n needs polynomials of degree Ω(√n).
Direct measurement of nonlinear properties of bipartite quantum states
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Information-Theoretic Lower Bounds for Approximating Monomials via Optimal Quantum Tsallis Entropy Estimation
A quantum estimator achieves near-optimal query complexity for integer-order Tsallis entropy, and the same technique yields a new information-theoretic proof that approximating x^n needs polynomials of degree Ω(√n).