Tightness of and counterexamples to several quantum estimates
Joseph Slote, Alexander Volberg, Haonan Zhang
Abstract
We prove here several tightness results for such quantum inequalities as the comparison of operator norm and product norm of d-local hamiltonians, Bohnenblust--Hille inequality for d-local hamiltonians and for quantum Fourier entropy-influence conjecture, we also discuss the quantum Aaronson--Ambainis conjecture in a special case of anti-commuting Pauli strings.
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